# SIST EN ISO 12213-3:2009

(Main)## Natural gas - Calculation of compression factor - Part 3: Calculation using physical properties (ISO 12213-3:2006)

## Natural gas - Calculation of compression factor - Part 3: Calculation using physical properties (ISO 12213-3:2006)

ISO 12213 specifies methods for the calculation of compression factors of natural gases, natural gases containing a synthetic admixture and similar mixtures at conditions under which the mixture can exist only as a gas. This part of ISO 12213 specifies a method for the calculation of compression factors when the superior calorific value, relative density and carbon dioxide content are known, together with the relevant pressures and temperatures. If hydrogen is present, as is often the case for gases with a synthetic admixture, the hydrogen content also needs to be known. The method is primarily applicable to pipeline quality gases within the ranges of pressure p and temperature T at which transmission and distribution operations normally take place, with an uncertainty of about ± 0,1 %. For wider-ranging applications the uncertainty of the results increases (see Annex F). More detail concerning the scope and field of application of the method is given in ISO 12213-1.

## Erdgas - Berechnung von Realgasfaktoren - Teil 3: Berechnungen basierend auf physikalischen Stoffeigenschaften als Eingangsgrößen (ISO 12213-3:2006)

Die Internationale Norm ISO 12213 legt für Erdgase, Erdgase mit synthetischen Beimischungen und ähnliche

Gemische Verfahren zur Berechnung der Realgasfaktoren unter Bedingungen fest, unter denen das Gemisch

nur als Gas existieren kann.

In diesem Teil von ISO 12213 wird ein Verfahren zur Berechnung der Realgasfaktoren für Gase festgelegt,

deren Brennwert, relative Dichte und Kohlenstoffdioxidgehalt ebenso wie die zutreffenden Drücke und

Temperaturen bekannt sind. Falls Wasserstoff vorhanden ist, was bei Gasen mit einer synthetischen

Beimischung häufig vorkommt, muss auch der Wasserstoffgehalt bekannt sein.

ANMERKUNG Der Realgasfaktor kann prinzipiell errechnet werden, wenn von den Parametern Brennwert, relative

Dichte, Kohlenstoffdioxidgehalt und Stickstoffgehalt drei bekannt sind (üblicherweise die drei Erstgenannten); es wird

jedoch davon abgeraten, den Stickstoffgehalt als Berechnungsparameter anzuwenden.

Auf aufbereitete Erdgase ist das Verfahren innerhalb der Bereiche für den Druck p und die Temperatur T, bei

denen Transport- und Verteilungsvorgänge üblicherweise ablaufen, vorrangig mit einer Unsicherheit von etwa

± 0,1 % anwendbar. Für erweiterte Anwendungsbereiche erhöht sich die Ergebnisunsicherheit (siehe

Anhang F).

Weitere Angaben zum Geltungs- und Anwendungsbereich des Verfahrens sind in ISO 12213-1 enthalten.

## Gaz naturel - Calcul du facteur de compression - Partie 3: Calcul à partir des caractéristiques physiques (ISO 12213-3:2006)

L'ISO 12213 spécifie des méthodes pour le calcul des facteurs de compression des gaz naturels, des gaz naturels contenant un adjuvant synthétique et de mélanges similaires dans des conditions telles que le mélange ne peut exister que sous forme gazeuse.

Elle est divisée en trois parties: la présente partie, l'ISO 12213-3:2006, spécifie une méthode pour le calcul des facteurs de compression lorsque le pouvoir calorifique supérieur, la densité relative et la teneur en dioxyde de carbone sont connus, ainsi que les pressions et les températures correspondantes. Lorsque l'hydrogène est présent, comme c'est souvent le cas dans les gaz présentant un adjuvant synthétique, il est aussi nécessaire de connaître la teneur en hydrogène.

La méthode est applicable principalement au gaz de qualité réseau dans les plages de pression, p, et de température, T, dans lesquelles s'effectuent normalement les opérations de transport et de distribution, avec une incertitude d'environ +/- 0,1 %. Dans le cas d'applications avec des plages plus étendues, l'incertitude des résultats augmente.

## Zemeljski plin - Izračun kompresijskega faktorja - 3. del: Izračun na podlagi fizikalnih lastnosti (ISO 12213-3:2006)

### General Information

### Relations

### Standards Content (Sample)

SLOVENSKI STANDARD

SIST EN ISO 12213-3:2009

01-november-2009

1DGRPHãþD

SIST EN ISO 12213-3:2005

=HPHOMVNLSOLQ,]UDþXQNRPSUHVLMVNHJDIDNWRUMDGHO,]UDþXQQDSRGODJL

IL]LNDOQLKODVWQRVWL,62

Natural gas - Calculation of compression factor - Part 3: Calculation using physical

properties (ISO 12213-3:2006)Erdgas - Berechnung von Realgasfaktoren - Teil 3: Berechnungen basierend auf

physikalischen Stoffeigenschaften als Eingangsgrößen (ISO 12213-3:2006)

Gaz naturel - Calcul du facteur de compression - Partie 3: Calcul à partir des

caractéristiques physiques (ISO 12213-3:2006)

Ta slovenski standard je istoveten z: EN ISO 12213-3:2009

ICS:

75.060 Zemeljski plin Natural gas

SIST EN ISO 12213-3:2009 en

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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SIST EN ISO 12213-3:2009

EUROPEAN STANDARD

EN ISO 12213-3

NORME EUROPÉENNE

EUROPÄISCHE NORM

September 2009

ICS 75.060 Supersedes EN ISO 12213-3:2005

English Version

Natural gas - Calculation of compression factor - Part 3:

Calculation using physical properties (ISO 12213-3:2006)

Gaz naturel - Calcul du facteur de compression - Partie 3: Erdgas - Berechnung von Realgasfaktoren - Teil 3:

Calcul à partir des caractéristiques physiques (ISO 12213- Berechnungen basierend auf physikalischen

3:2006) Stoffeigenschaften als Eingangsgrößen (ISO 12213-3:2006)

This European Standard was approved by CEN on 13 August 2009.

CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European

Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such national

standards may be obtained on application to the CEN Management Centre or to any CEN member.

This European Standard exists in three official versions (English, French, German). A version in any other language made by translation

under the responsibility of a CEN member into its own language and notified to the CEN Management Centre has the same status as the

official versions.CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Cyprus, Czech Republic, Denmark, Estonia, Finland,

France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal,

Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom.EUROPEAN COMMITTEE FOR STANDARDIZATION

COMITÉ EUROPÉEN DE NORMALISATION

EUROPÄISCHES KOMITEE FÜR NORMUNG

Management Centre: Avenue Marnix 17, B-1000 Brussels

© 2009 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 12213-3:2009: E

worldwide for CEN national Members.---------------------- Page: 3 ----------------------

SIST EN ISO 12213-3:2009

EN ISO 12213-3:2009 (E)

Contents Page

Foreword ..............................................................................................................................................................3

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EN ISO 12213-3:2009 (E)

Foreword

The text of ISO 12213-3:2006 has been prepared by Technical Committee ISO/TC 193 “Natural gas” of the

International Organization for Standardization (ISO) and has been taken over as EN ISO 12213-3:2009.

This European Standard shall be given the status of a national standard, either by publication of an identical

text or by endorsement, at the latest by March 2010, and conflicting national standards shall be withdrawn at

the latest by March 2010.Attention is drawn to the possibility that some of the elements of this document may be the subject of patent

rights. CEN [and/or CENELEC] shall not be held responsible for identifying any or all such patent rights.

This document supersedes EN ISO 12213-3:2005.According to the CEN/CENELEC Internal Regulations, the national standards organizations of the following

countries are bound to implement this European Standard: Austria, Belgium, Bulgaria, Cyprus, Czech

Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia,

Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain,

Sweden, Switzerland and the United Kingdom.Endorsement notice

The text of ISO 12213-3:2006 has been approved by CEN as a EN ISO 12213-3:2009 without any

modification.---------------------- Page: 5 ----------------------

SIST EN ISO 12213-3:2009

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SIST EN ISO 12213-3:2009

INTERNATIONAL ISO

STANDARD 12213-3

Second edition

2006-11-15

Natural gas — Calculation of

compression factor —

Part 3:

Calculation using physical properties

Gaz naturel — Calcul du facteur de compression —

Partie 3: Calcul à partir des caractéristiques physiques

Reference number

ISO 12213-3:2006(E)

ISO 2006

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SIST EN ISO 12213-3:2009

ISO 12213-3:2006(E)

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Published in Switzerland

ii © ISO 2006 – All rights reserved

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SIST EN ISO 12213-3:2009

ISO 12213-3:2006(E)

Contents Page

Foreword............................................................................................................................................................ iv

1 Scope ..................................................................................................................................................... 1

2 Normative references ........................................................................................................................... 1

3 Terms and definitions........................................................................................................................... 1

4 Method of calculation........................................................................................................................... 2

4.1 Principle................................................................................................................................................. 2

4.2 The SGERG-88 equation ...................................................................................................................... 2

4.3 Input variables....................................................................................................................................... 3

4.4 Ranges of application........................................................................................................................... 3

4.5 Uncertainty ............................................................................................................................................ 5

5 Computer program ............................................................................................................................... 6

Annex A (normative) Symbols and units......................................................................................................... 7

Annex B (normative) Description of the SGERG-88 method....................................................................... 10

Annex C (normative) Example calculations .................................................................................................. 21

Annex D (normative) Conversion factors ...................................................................................................... 22

Annex E (informative) Specification for pipeline quality natural gas ......................................................... 25

Annex F (informative) Performance over wider ranges of application ....................................................... 28

Annex G (informative) Subroutine SGERG.FOR in Fortran ......................................................................... 33

Bibliography ..................................................................................................................................................... 38

© ISO 2006 – All rights reserved iii---------------------- Page: 9 ----------------------

SIST EN ISO 12213-3:2009

ISO 12213-3:2006(E)

Foreword

ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies

(ISO member bodies). The work of preparing International Standards is normally carried out through ISO

technical committees. Each member body interested in a subject for which a technical committee has been

established has the right to be represented on that committee. International organizations, governmental and

non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the

International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.

International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.

The main task of technical committees is to prepare International Standards. Draft International Standards

adopted by the technical committees are circulated to the member bodies for voting. Publication as an

International Standard requires approval by at least 75 % of the member bodies casting a vote.

Attention is drawn to the possibility that some of the elements of this document may be the subject of patent

rights. ISO shall not be held responsible for identifying any or all such patent rights.

ISO 12213-3 was prepared by Technical Committee ISO/TC 193, Natural gas, Subcommittee SC 1, Analysis

of natural gas.This second edition cancels and replaces the first edition (ISO 12213-3:1997), which has been technically

revised. The revision includes changes to Subclause 4.4.1 and the addition of a new annex, Annex E.

ISO 12213 consists of the following parts, under the general title Natural gas — Calculation of compression

factor:⎯ Part 1: Introduction and guidelines

⎯ Part 2: Calculation using molar-composition analysis

⎯ Part 3: Calculation using physical properties

iv © ISO 2006 – All rights reserved

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SIST EN ISO 12213-3:2009

INTERNATIONAL STANDARD ISO 12213-3:2006(E)

Natural gas — Calculation of compression factor —

Part 3:

Calculation using physical properties

1 Scope

ISO 12213 specifies methods for the calculation of compression factors of natural gases, natural gases

containing a synthetic admixture and similar mixtures at conditions under which the mixture can exist only as a

gas.This part of ISO 12213 specifies a method for the calculation of compression factors when the superior

calorific value, relative density and carbon dioxide content are known, together with the relevant pressures

and temperatures. If hydrogen is present, as is often the case for gases with a synthetic admixture, the

hydrogen content also needs to be known.NOTE In principle, it is possible to calculate the compression factor when any three of the parameters superior

calorific value, relative density, carbon dioxide content (the usual three) and nitrogen content are known, but subsets

including nitrogen content are not recommended.The method is primarily applicable to pipeline quality gases within the ranges of pressure p and temperature T

at which transmission and distribution operations normally take place, with an uncertainty of about ± 0,1 %.

For wider-ranging applications the uncertainty of the results increases (see Annex F).

More detail concerning the scope and field of application of the method is given in ISO 12213-1.

2 Normative referencesThe following referenced documents are indispensable for the application of this document. For dated

references, only the edition cited applies. For undated references, the latest edition of the referenced

document (including any amendments) applies.ISO 6976:1995, Natural gas — Calculation of calorific values, density, relative density and Wobbe index from

compositionISO 12213-1, Natural gas — Calculation of compression factor — Part 1: Introduction and guidelines

ISO 80000-4, Quantities and units — Part 4: MechanicsISO 80000-5, Quantities and units — Part 5: Thermodynamics

3 Terms and definitions

For the purposes of this document, the terms and definitions given in ISO 12213-1 apply.

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SIST EN ISO 12213-3:2009

ISO 12213-3:2006(E)

4 Method of calculation

4.1 Principle

The method recommended uses equations which are based on the concept that pipeline quality natural gas

may be uniquely characterized for calculation of its volumetric properties by an appropriate and distinctive set

of measurable physical properties. These characteristics, together with the pressure and temperature, are

used as input data for the method.The method uses the following physical properties: superior calorific value, relative density and carbon dioxide

content. The method is particularly useful in the common situation where a complete molar composition is not

available, but may also be preferred for its relative simplicity. For gases with a synthetic admixture, the

hydrogen content needs to be known.4.2 The SGERG-88 equation

The calculation method using physical properties is based on the standard GERG 88 (SGERG-88) virial

[1], [2], [3]equation for natural gases . The standard GERG 88 virial equation is derived from the master

GERG 88 (MGERG-88) virial equation, which is a method of calculation based on a molar-composition

[4]analysis .

The SGERG-88 virial equation from which the compression factor Z is calculated may be written as

ZB=+1 ρ +Cρ (1)where

B and C are functions of the input data comprising the superior calorific value H , the relative density d,

the contents of both inert and combustible non-hydrocarbon components of the gas mixture

(CO and H ) and the temperature T;2 2

ρ is the molar density given by

ρ = p ZRT (2)

( )

where

Z = f (p, T, H , d, x , x) (3)

1 S CO H

2 2

However, the SGERG-88 method treats the natural-gas mixture internally as a five-component mixture

consisting of an equivalent hydrocarbon gas (with the same thermodynamic properties as the sum of the

hydrocarbons present), nitrogen, carbon dioxide, hydrogen and carbon monoxide. To characterize the

thermodynamic properties of the hydrocarbon gas adequately, the hydrocarbon heating value H is also

needed. Therefore, the calculation of Z usesZ = f (p, T, H , x , x , x , x , x) (4)

2 CH CH N CO H CO

2 2 2

In order to be able to model coke oven gas mixtures, the mole fraction of carbon monoxide is taken to have a

fixed relation to the hydrogen content. If hydrogen is not present (x < 0,001), then set x = 0. The natural-

H H2 2

gas mixture is then treated in the calculation method as a three-component mixture (see Annex B).

The calculation is performed in three steps:First, the five-component composition from which both the known superior calorific value and the known

relative density can be calculated satisfactorily may be found from the input data by an iterative procedure

described in detail in Annex B.Secondly, once this composition is known, B and C may be found using relationships also given in Annex B.

2 © ISO 2006 – All rights reserved---------------------- Page: 12 ----------------------

SIST EN ISO 12213-3:2009

ISO 12213-3:2006(E)

In the third step, Equations (1) and (2) are solved simultaneously for ρ and Z by a suitable numerical

method.A flow diagram of the procedure for calculating Z from the input data is shown in Figure B.1.

4.3 Input variables4.3.1 Preferred input data set

The input variables required for use with the SGERG-88 equation are the absolute pressure, temperature and

superior calorific value (volumetric basis), the relative density, the carbon dioxide content and the hydrogen

content. Thus the physical properties used in the input data set (set A) areH , d, x and x

S CO H

2 2

Relative density is referred to normal conditions (101,325 kPa and 0 °C) and superior calorific value is referred

to normal conditions (101,325 kPa and 0 °C) and a combustion temperature of 25 °C.

4.3.2 Alternative input data setsThree alternatives to the preferred input data set (see 4.3.1) may be used with the standard GERG 88 virial

equation:x , H , d and x (set B)

N S H

2 2

x , x , d and x (set C)

N CO H

2 2 2

x , x , H and x (set D)

N CO S H

2 2 2

[3]

The alternative input data sets are considered fully in GERG Technical Monograph TM5 . Use of the

alternative input data sets gives results which may differ at the fourth decimal place. This part of ISO 12213

recommends the use of input data set A.4.4 Ranges of application

4.4.1 Pipeline quality gas

The ranges of application for pipeline quality gas are as defined below:

absolute pressure 0 MPa u p u 12 MPa

temperature 263 K u T u 338 K

mole fraction of carbon dioxide 0 u x u 0,20

mole fraction of hydrogen 0 u x u 0,10

−3 −3

superior calorific value 30 MJ⋅m u H u 45 MJ⋅m

relative density 0,55 u d u 0,80

The mole fractions of other natural-gas components are not required as input. These mole fractions shall,

however, lie within the following ranges (the ratio of successive mole fractions in the alkane homologous

series is typically 3:1 — see Annex E):methane 0,7 u x u 1,0

nitrogen 0 u x u 0,20

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SIST EN ISO 12213-3:2009

ISO 12213-3:2006(E)

ethane 0 u x u 0,10

C H

2 6

propane 0 u x u 0,035

C H

3 8

butanes 0 u x u 0,015

C H

4 10

pentanes 0 u x u 0,005

C H

5 12

hexanes 0 u x u 0,001

heptanes 0 u x u 0,000 5

octanes plus higher hydrocarbons 0 u x u 0,000 5

carbon monoxide 0 u x u 0,03

helium 0 u x u 0,005

water 0 u x u 0,000 15

H O

The method applies only to mixtures in the single-phase gaseous state (above the dew point) at the conditions

of temperature and pressure of interest. For pipeline quality gas, the method is applicable over wider ranges

of temperature and pressure but with increased uncertainty (see Figure 1). In the computer implementation,

the lower temperature limit is set at 250 K.4.4.2 Wider ranges of application

The ranges of application tested beyond the limits given in 4.4.1 are:

absolute pressure 0 MPa u p u 12 MPa

temperature 263 K u T u 338 K

mole fraction of carbon dioxide 0 u x u 0,30

mole fraction of hydrogen 0 u x u 0,10

−3 −3

superior calorific value 20 MJ⋅m u H u 48 MJ⋅m

relative density 0,55 u d u 0,90

The allowable mole fractions of other major natural-gas components are extended to:

methane 0,5 u x u 1,0nitrogen 0 u x u 0,50

ethane 0 u x u 0,20

C H

2 6

propane 0 u x u 0,05

C H

3 8

The limits for other minor natural-gas components remain as given in 4.4.1 for pipeline quality gas.

The method is not applicable outside these ranges; the computer implementation described in Annex B will

not allow violation of the limits of composition quoted here.4 © ISO 2006 – All rights reserved

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SIST EN ISO 12213-3:2009

ISO 12213-3:2006(E)

4.5 Uncertainty

4.5.1 Uncertainty for pipeline quality gas

The uncertainty in the prediction of the compression factor ∆Z (for the temperature range 263 K to 338 K) is

± 0,1 % at pressures up to 10 MPa and ± 0,2 % between 10 MPa and 12 MPa for natural gases with

−3 −3x u 0,20, x u 0,09, x u 0,10 and x u 0,10, and for 30 MJ⋅m u H u 45 MJ⋅m and

N CO C H H S

2 2 2 6 2

0,55 u d u 0,80 (see Figure 1).

For gases with a CO content exceeding a mole fraction of 0,09, the uncertainty of ± 0,1 % is maintained for

pressures up to 6 MPa and for temperatures between 263 K and 338 K. This uncertainty level is determined

[5], [6]by comparison with the GERG databank on measurements of the compression factor for natural gases

[9]and with the Gas Research Institute data .

SGERG-88 equation

Key

p pressure

T temperature

1 ∆Z u ± 0,1 %

2 ∆Z ± 0,1 % to ± 0,2 %

3 ∆Z ± 0,2 % to ± 0,5 %

4 ∆Z ± 0,5 % to ± 3,0 %

Figure 1 — Uncertainty limits for the calculation of compression factors

(The uncertainty limits given are expected to be valid for natural gases and similar gases with x u 0,20;

−3 −3x u 0,09; x u 0,10 and x u 0,10, and for 30 MJ⋅m u H u 45 MJ⋅m and 0,55 u d u 0,80)

CO C H H S2 2 6 2

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SIST EN ISO 12213-3:2009

ISO 12213-3:2006(E)

4.5.2 Uncertainty for wider ranges of application

The estimated uncertainties involved in calculations of compression factors beyond the limits of quality given

in 4.5.1 are discussed in Annex F.4.5.3 Impact of uncertainties of input variables

Listed in Table 1 are typical values for the uncertainties of the relevant input variables. These values may be

achieved under optimum operating conditions.As a general guideline only, an error propagation analysis using the above uncertainties in the input variables

produces an additional uncertainty of about ± 0,1 % in the result at 6 MPa and within the temperature range

263 K to 338 K. Above 6 MPa, the additional uncertainties are greater and increase roughly in direct

proportion to the pressure (see Reference [3]).4.5.4 Reporting of results

Results for the compression factor shall be reported to four places of decimals, together with the pressure and

temperature values and the calculation method used (ISO 12213-3, SGERG-88 equation). For verification of

calculation procedures, it is useful to carry extra digits.Table 1 — Uncertainties of input variables

Input variable Absolute uncertainty

Absolute pressure ± 0,02 MPa

Temperature ± 0,15 K

Mole fraction of carbon dioxide ± 0,002

Mole fraction of hydrogen ± 0,005

Relative density ± 0,001 3

Superior calorific value ± 0,06 MJ⋅m

5 Computer program

Software which implements this International Standard has been prepared. Users of this part of ISO 12213

are invited to contact ISO/TC 193/SC 1, either directly or through their ISO member body, to enquire about the

availability of this software.6 © ISO 2006 – All rights reserved

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SIST EN ISO 12213-3:2009

ISO 12213-3:2006(E)

Annex A

(normative)

Symbols and units

The symbols specified in this annex are those which are used in both the main text and in Annex B. The units

specified here are those which give consistency with the values of the coefficients given in Annex B.

Symbol Meaning Units3 −1

b Zero-order (constant) term in the molar heating value (H ) expansion of B m⋅kmol

H0 CH 11[Equation (B.20)]

3 −1

b First-order (linear) term in the molar heating value (H ) expansion of B m⋅MJ

H1 CH 11

[Equation (B.20)]

3 −2

b Second-order (quadratic) term in the molar heating value (H ) expansion m⋅kmol⋅MJ

H2 CHof B [Equation (B.20)]

3 −1

m⋅kmol

b (0)⎫

H 0

3 −1 −1

b (1) m⋅kmol ⋅K

Terms in the temperature expansion of b [Equation (B.21)]

H 0

3 −1 −2

b (2)

m⋅kmol ⋅K

H 0 ⎭

3 −1

m⋅MJ

b (0)⎫

3 −1 −1

m⋅MJ ⋅K

b (1) Terms in the temperature expansion of b [Equation (B.21)]

3 −1 −2

b (2)

m⋅MJ ⋅K

H1 ⎭

3 −2

m⋅kmol⋅MJ

b (0)⎫

H 2

3 −2 −1

b (1) m⋅kmol⋅MJ ⋅K

Terms in the temperature expansion of b [Equation (B.21)]

H 2

3 −2 −2

b (2)

m⋅kmol⋅MJ ⋅K

H 2 ⎭

3 −1

m⋅kmol

b (0)

3 −1 −1

b (1) m⋅kmol ⋅K

Terms in the temperature expansion of b [Equation (B.22)]

b (2) 3 −1 −2

⎪ m⋅kmol ⋅K

3 −1

B Second virial coefficient [Equation (1)] m⋅kmol

3 −1

B Second virial coefficient for binary interaction between component i and m⋅kmol

component j [Equation (B.22)]6 −2

c Zero-order (constant) term in the molar heating value (H ) expansion of m⋅kmol

H0 CH

C [Equation (B.29)]

111

6 −1 −1

c First-order (linear) term in the molar heating value (H ) expansion of m⋅kmol ⋅MJ

H1 CHC [Equation (B.29)]

111

6 −2

c Second-order (quadratic) term in the molar heating value (H ) expansion m⋅MJ

H2 CH

of C [Equation (B.29)]

111

© ISO 2006 – All rights reserved 7

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SIST EN ISO 12213-3:2009

ISO 12213-3:2006(E)

Symbol Meaning Units

6 −2

m⋅kmol

c (0)⎫

H 0

6 −2 −1

c (1) m⋅kmol ⋅K

Terms in the temperature expansion of c [Equation (B.30)]

H 0

6 −2 −2

c (2)

m⋅kmol ⋅K

H 0 ⎭

6 −1 −1

m⋅kmol ⋅MJ

c (0)⎫

6 −1 −1 −1

m⋅kmol ⋅MJ ⋅K

c (1) Terms in the temperature expansion of c [Equation (B.30)]

6 −1 −1 −2

c (2)

m⋅kmol ⋅MJ ⋅K

H1 ⎭

6 −2

m⋅MJ

c (0)⎫

H 2

6 −2 −1

c (1) m⋅MJ ⋅K

Terms in the temperature expansion of c [Equation (B.30)]

H 2

6 −2 −2

c (2)

m⋅MJ ⋅K

H 2 ⎭

6 −2

m⋅kmol

c (0)

ijk

6 −2 −1

c (1) m⋅kmol ⋅K

Terms in the temperature expansion of c [Equation (B.31)]

ijk

ijk

c (2)

6 −2 −2

ijk

⎪ m⋅kmol ⋅K

6 −2

C Third virial coefficient [Equation (1)] m⋅kmol

6 −2

C Third virial coefficient for ternary interaction between components i, j m⋅kmol

ijkand k [Equation (B.31)]

d Relative density [d(air) = 1; Equation (B.1)] —

DH Change in the molar heating value H during iteration MJ⋅kmol

CH CH

[Equations (B.10) and (B.11)]

H Superior calorific value [gas at normal conditions (0 °C, 1,013 25 bar), MJ⋅m

combustion temperature 25 °C]

H Molar heating value (combustion temperature 25 °C) MJ⋅kmol

M Molar mass [Equations (B.5) and (B.8)] kg⋅kmol

p Absolute pressure bar

3 −1 −1

R (Universal) gas constant m⋅bar⋅kmol ⋅K

T Absolute temperature K

t Celsius temperature [= T − 273,15; Equation (B.27)] °C

3 −1

V Molar volume (= 1/ρ) m⋅kmol

m m

x Mole fraction of a component —

y Combination rule parameters for the binary unlike-interaction virial —

coefficients B and B (Table B.2) and the ternary unlike-interaction

12 13

virial coefficient C [Equation (B.32)]

ijk

Z Compression factor —

ρ Mass density [Equations (B.8) and (B.42)] kg⋅m

−1 −3

ρ Molar density (= V) kmol⋅m

m m

8 © ISO 2006 – All rights reserved

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SIST EN ISO 12213-3:2009

ISO 12213-3:2006(E)

Additional subscripts

n Value at normal conditions (T = 273,15 K, p = 1,013 25 bar)

n n

CH For the equivalent hydrocarbon

CO For carbon monoxide

CO For carbon dioxide

H For hydrogen

N For nitrogen

Additional qualifiers

(air) For dry air of standard composition [Equation (B.1)]

(D) For special value of ρ used in Equation (B.11)

1 For the equivalent hydrocarbon [Equations (B.12) and (B.15)]

2 For nitrogen [Equations (B.12) and (B.16)]

3 For carbon dioxide [Equations (B.12) and (B.17)]

4 For hydrogen [Equations (B.12) and (B.18)]

5 For carbon monoxide [Equations (B.12) and (B.19)]

(id) Ideal gas state

(u) Iteration counter (B.2.1)

(v) Iteration counter (B.2.2)

(w) Iteration counter (B.4)

© ISO 2006 – All rights reserved 9

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SIST EN ISO 12213-3:2009

ISO 12213-3:2006(E)

Annex B

(normative)

Description of the SGERG-88 method

This annex gives the equations for, and numerical values of, coefficients which together specify completely

the SGERG method for calculation of compression factors.[3]

It also describes iteration procedures adopted by GERG for implementing the method in the verified

Fortran 77 subroutine SGERG.FOR. This subroutine provides the correct solution; other computational

procedures are acceptable provided that they can be demonstrated to yield identical numerical results. The

calculated results shall agree to at least the fourth place of decimals with the examples given in Annex C.

Other implementations which are known to produce identical results are as follows:

[3]a) A BASIC version, described in GERG TM5 , which may be used with a variety of metric reference

conditions. This programme was designed mainly for PC applications.[8]

b) A version in C, described in German DVGW Directives, sheet G486 .

c) A version in Turbo Pascal.

All these programmes have been verified to give the same results to within 10 . The availability of the

programmes and the conditions which apply to their use are discussed in Part 1 of this

**...**

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