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.
It is divided into three parts: this part, ISO 12213-3:2006, 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.
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
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
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
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.
Contents Page
Foreword .3
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.
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
ISO 12213-3:2006(E)
PDF disclaimer
This PDF file may contain embedded typefaces. In accordance with Adobe's licensing policy, this file may be printed or viewed but
shall not be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In
downloading this file, parties accept therein the responsibility of not infringing Adobe's licensing policy. The ISO Central Secretariat
accepts no liability in this area.
Adobe is a trademark of Adobe Systems Incorporated.
Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation
parameters were optimized for printing. Every care has been taken to ensure that the file is suitable for use by ISO member bodies. In
the unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below.
© ISO 2006
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means,
electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or
ISO's member body in the country of the requester.
ISO copyright office
Case postale 56 • CH-1211 Geneva 20
Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
E-mail copyright@iso.org
Web www.iso.org
Published in Switzerland
ii © ISO 2006 – All rights reserved
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 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
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 references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
ISO 6976:1995, Natural gas — Calculation of calorific values, density, relative density and Wobbe index from
composition
ISO 12213-1, Natural gas — Calculation of compression factor — Part 1: Introduction and guidelines
ISO 80000-4, Quantities and units — Part 4: Mechanics
ISO 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.
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)
mm
where
B and C are functions of the input data comprising the superior calorific value H , the relative density d,
S
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
m
ρ = p ZRT (2)
( )
m
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
CH
needed. Therefore, the calculation of Z uses
Z = 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 H
2 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
ISO 12213-3:2006(E)
In the third step, Equations (1) and (2) are solved simultaneously for ρ and Z by a suitable numerical
m
method.
A flow diagram of the procedure for calculating Z from the input data is shown in Figure B.1.
4.3 Input variables
4.3.1 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) are
H , 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 sets
Three 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
CO
mole fraction of hydrogen 0 u x u 0,10
H
−3 −3
superior calorific value 30 MJ⋅m u H u 45 MJ⋅m
S
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
CH
nitrogen 0 u x u 0,20
N
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
C
heptanes 0 u x u 0,000 5
C
octanes plus higher hydrocarbons 0 u x u 0,000 5
C
8+
carbon monoxide 0 u x u 0,03
CO
helium 0 u x u 0,005
He
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
CO
mole fraction of hydrogen 0 u x u 0,10
H
−3 −3
superior calorific value 20 MJ⋅m u H u 48 MJ⋅m
S
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 1,0
CH
nitrogen 0 u x u 0,50
N
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
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 −3
x 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;
N
−3 −3
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 0,55 u d u 0,80)
CO C H H S
2 2 6 2
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
−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
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 Units
3 −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 CH
of 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
H0
⎪
3 −1 −2
b (2)
m⋅kmol ⋅K
H 0 ⎭
3 −1
m⋅MJ
b (0)⎫
H1
⎪
3 −1 −1
m⋅MJ ⋅K
b (1) Terms in the temperature expansion of b [Equation (B.21)]
⎬
H1
H1
⎪
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
H2
⎪
3 −2 −2
b (2)
m⋅kmol⋅MJ ⋅K
H 2 ⎭
3 −1
m⋅kmol
⎫
b (0)
ij
⎪
⎪
3 −1 −1
b (1) m⋅kmol ⋅K
Terms in the temperature expansion of b [Equation (B.22)]
⎬
ij
ij
⎪
b (2) 3 −1 −2
ij
⎪ 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
ij
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)]
6 −1 −1
c First-order (linear) term in the molar heating value (H ) expansion of m⋅kmol ⋅MJ
H1 CH
C [Equation (B.29)]
6 −2
c Second-order (quadratic) term in the molar heating value (H ) expansion m⋅MJ
H2 CH
of C [Equation (B.29)]
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
H0
⎪
6 −2 −2
c (2)
m⋅kmol ⋅K
H 0 ⎭
6 −1 −1
m⋅kmol ⋅MJ
c (0)⎫
H1
⎪
6 −1 −1 −1
m⋅kmol ⋅MJ ⋅K
c (1) Terms in the temperature expansion of c [Equation (B.30)]
⎬
H1
H1
⎪
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
H2
⎪
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
ijk
and k [Equation (B.31)]
d Relative density [d(air) = 1; Equation (B.1)] —
−1
DH Change in the molar heating value H during iteration MJ⋅kmol
CH CH
[Equations (B.10) and (B.11)]
−3
H Superior calorific value [gas at normal conditions (0 °C, 1,013 25 bar), MJ⋅m
S
combustion temperature 25 °C]
−1
H Molar heating value (combustion temperature 25 °C) MJ⋅kmol
−1
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 —
−3
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
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 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.
−5
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 International Standard.
B.1 Basic structure of the calculation method
As described in 4.2, the calculation proceeds in three steps, which are shown schematically in Figure B.1.
10 © ISO 2006 – All rights reserved
ISO 12213-3:2006(E)
Figure B.1 — Flow diagram for standard GERG-88 calculation method
(x = mole fraction of component i)
i
The calculation is described below in the order in which these three steps are carried out.
Step I
The input data are pressure, temperature, gross calorific value, relative density and the mole fractions of
carbon dioxide and hydrogen. If the values of the first three parameters are in any units other than bar, °C and
3 3
MJ/m , they shall first be converted precisely to values in bar, °C and MJ/m , respectively, using the
guidelines set out in Annex D.
The input data are then used to calculate the following intermediate data:
Mole fraction of:
hydrocarbon gas x
CH
nitrogen x
N
carbon monoxide x
CO
Molar heating value of the equivalent hydrocarbon H
CH
ISO 12213-3:2006(E)
Molar mass of the equivalent hydrocarbon M
CH
Second virial coefficient (T = 273,15 K) B
n n
Molar density at normal conditions ρ
m,n
Mass density at normal conditions ρ
n
Superior calorific value of the gas H
S
In Equations (B.1) to (B.46), each symbol represents a physical quantity divided by its selected unit
(see Annex A), such that their quotient is the dimensionless value of the quantity.
Step II
The intermediate data are used to calculate the second and third virial coefficients for the natural gas at the
required temperature, B(T,H ,x ) and C(T,H ,x ).
CH i CH i
Step III
The second and third virial coefficients determined in the second step are inserted in the virial equation, and
the compression factor Z is calculated for a given pressure and temperature.
The symbols used are defined in Annex A.
B.2 Calculation of intermediate data
The eight intermediate-data values (x , x , x , H , M , B , ρ , ρ ) are determined from
CH N CO CH CH n m,n n
Equations (B.1) to (B.8) using the iterative method presented in Figure B.2. Values of the constants used in
these equations are given in Table B.1.
ρρ= d (air) (B.1)
nn
xx= 0,096 4 (B.2)
CO H2
VR(id)=Tp (B.3)
m,n n n
−1
⎡⎤
ρ ()vV=+(id) B ()v (B.4)
m,n m,n n
⎣⎦
Mu( )=− 2,709 328+ 0,021062 199H (u− 1) (B.5)
CH CH
⎡⎤
⎡⎤
xu()=−H H (u 1)ρ (v)− x H+x H H (u−1) (B.6)
()
CH S CH m,n H H CO CO CH
⎣⎦
⎢⎥22
⎣⎦
xu()=−1 x (u)−x −x −x (B.7)
NCH COHCO
⎡⎤
ρρ(ux)=+()uM ()u x ()uM (v)+x M+x M+x Mρ (v) (B.8)
( )
n CH CH N N m,n CO CO H H CO CO m,n
⎣⎦22 2 2 2 2
12 © ISO 2006 – All rights reserved
ISO 12213-3:2006(E)
Figure B.2 — Flow diagram for computing intermediate data by iteration
ISO 12213-3:2006(E)
Table B.1 — Values of the constants used in Equations (B.1) to (B.8)
(adjusted to conform with the molar masses and molar calorific values in ISO 6976:1995)
−1
H = 285,83 MJ⋅kmol
H
−1
H = 282,98 MJ⋅kmol
CO
−1
M = 28,013 5 kg⋅kmol
N
−1
M = 44,010 kg⋅kmol
CO
−1
M = 2,015 9 kg⋅kmol
H
−1
M = 28,010 kg⋅kmol
CO
3 −1 −1
R = 0,083 145 1 m ⋅bar⋅kmol ⋅K
3 −1
V (id) = 22,414 097 m ⋅kmol
m,n
−3
ρ (air) = 1,292 923 kg⋅m
n
B.2.1 Iteration with the molar heating value H (inner loop)
CH
Equations (B.1) to (B.8) are applied in sequence so as to obtain the first approximation in the uth iteration step.
The starting values are:
−1
H (u = 0) = 1 000 MJ⋅kmol
CH
3 −1
B (v = 0) = − 0,065 m⋅kmol
n
The values of the other constants used in Equations (B.1) to (B.8) are given in Table B.1.
The convergence criterion for this inner iteration loop is that the absolute difference between the calculated
density of the gas at normal conditions ρ (u) and the known density (either measured directly or determined
n
−6
from the relative density) of the gas at normal conditions ρ is less than 10 , i.e.
n
−6
ρρ−
()
nn
If this condition is not satisfied, then an improved value of the molar heating value H (u), for use in
CH
Equations (B.5) to (B.8), is calculated using Equation (B.10) as follows:
H ()uH=−(u 1)+DH (u) (B.10)
CH CH CH
where
−1
⎡⎤
DH ()u=−⎡⎤ρρ ()u ρ D−ρ (u) (B.11)
()
CH⎣⎦n n n
⎣⎦
ρ (u) being the density value for the current iteration step [commencing with H (u − 1)],
n CH
ρ(D) being the density determined by Equations (B.4) to (B.8) using [H (u - 1) + 1] as input for
CH
the molar heating value.
−6
When the left-hand side of Equation (B.9) is less than 10 , this iteration loop is terminated and iteration with
the second virial coefficient begins.
14 © ISO 2006 – All rights reserved
ISO 12213-3:2006(E)
B.2.2 Iteration with the second virial coefficient B (outer loop)
n
The intermediate values x (u), x (u), x and H (u) from the preceding iteration and the input data x
CH N CO CH CO
2 2
and x are used to determine an improved value for the second virial coefficient B (v) for the whole gas at
H n
normal conditions.
The second virial coefficient for the natural gas is given by the following equation:
B()T=x B+2x x B++2x xB 2x x B++2x xB x B+2x x B+2x x B+
1 11 1 2 12 1 313 1 414 1 515 2 22 2 3 23 2 4 24
22 2
++xB x B+xB (B.12)
333 4 44 555
Some of the terms that are missing in Equation (B.12), i.e. B , B , etc., have been found not to improve the
25 34
accuracy of the calculation if included and are therefore set at zero.
B ()vB= T (B.13)
( )
nn
where
TT== 273,15 (B.14)
n
xx= ()u (B.15)
1 CH
xx= ()u (B.16)
2 N
xx= (B.17)
3 CO
xx= (B.18)
4 H
xx= (B.19)
5 CO
B=+bbH ()u+bH (u) (B.20)
11 HH0C1H H2CH
where the coefficients b , b and b are second-degree polynomials as a function of temperature
H0 H1 H2
⎡⎤
B=+bb(0) (1)T+b (2)T+b (0)+b (1)T+b (2)TH (u)+
11HH0 0 H0 H1 H1 H1 CH
⎣⎦
⎡⎤
++bb(0) (1)T+b (2)TH (u) (B.21)
HH22 H2 CH
⎣⎦
and the second virial coefficients B , B , B , B , B , B , B , B and B are also second-degree
14 15 22 23 24 33 34 44 55
polynomials as a function of temperature, in the general form
B=+bb(0) (1)T+b (2)T (B.22)
ij ij ij ij
The unlike-interaction virial coefficients B and B are given by
12 13
−52
⎡⎤
BT=+0,72 1,875× 10 (320− )B+B 2 (B.23)
()
12 11 22
⎣⎦
BB=− 0,865B (B.24)
()
13 11 33
The coefficients in Equations (B.21) to (B.24) are given in Table B.2.
ISO 12213-3:2006(E)
Table B.2 — Numerical values for the coefficients b(0), b(1) and b(2) in the temperature expansion of
the second virial coefficient for pure gases and of the unlike-interaction virial coefficients
3 −1
(The units of B are m⋅kmol when the temperature is in kelvins.)
ij b(0) b(1) b(2)
−1 −3 −6
CH H0 − 4,254 68 × 10 2,865 00 × 10 − 4,620 73 × 10
−4 −6 −9
CH H1 8,771 18 × 10 − 5,562 81 × 10 8,815 10 × 10
−7 −9 −12
CH H2 − 8,247 47 × 10 4,314 36 × 10 − 6,083 19 × 10
−1 −4 −7
N 22 − 1,446 00 × 10 7,409 10 × 10 − 9,119 50 × 10
−1 −3 −6
CO 33 − 8,683 40 × 10 4,037 60 × 10 − 5,165 70 × 10
−3 −5 −8
H 44 − 1,105 96 × 10 8,133 85 × 10 − 9,872 20 × 10
−1 −4 −7
CO 55 − 1,308 20 × 10 6,025 40 × 10 − 6,443 00 × 10
−5 2
CH + N 12 y = 0,72 + 1,875 × 10 (320 − T)
CH + CO 13 y = − 0,865
−2 −4 −7
CH + H 14 − 5,212 80 × 10 2,715 70 × 10 − 2,500 00 × 10
−2 −6 −7
CH + CO 15 − 6,872 90 × 10 − 2,393 81 × 10 5,181 95 × 10
−1 −3 −6
N + CO 23 − 3,396 93 × 10 1,611 76 × 10 − 2,044 29 × 10
2 2
−2
N + H 24 1,200 00 × 10 0,000 00 0,000 00
2 2
The value of B (v) obtained from Equation (B.13) is used to calculate the vth approximation of ρ using
n m,n
Equation (B.4).
Equation (B.6) is then used, in the inverse way to that in which it was used previously, to obtain a value for
H (v), i.e.
S
H ()vx=−⎡⎤(u)H (u 1)+xH+xH ρ (v) (B.25)
SC⎣⎦14H 455m,n
where H (= H ) and H (= H ) are the molar heating values at 298,15 K of hydrogen and carbon monoxide,
4 H 5 CO
respectively. The convergence criterion for the outer iteration loop (iteration counter v) is that the absolute
difference between the measured superior calorific value H and the calculated calorific value H (v) is less
S S
−4
than 10 , i.e.
−4
HH−<()v 10 (B.26)
SS
If this criterion is not satisfied, then the value for B (v) determined from Equation (B.13) is used as a new input
n
value for Equation (B.4) and the whole iteration procedure, i.e. the inner iteration loop (iteration counter u), is
restarted from Equation (B.5) using the current values of H (u − 1) and ρ (v).
CH m,n
When both convergence criterion (B.9) and convergence criterion (B.26) are satisfied simultaneously, the final
intermediate data for the mole fractions x and x and for the molar heating value H have been
CH N CH
determined.
B.3 Calculation of virial coefficients
The second and third virial coefficients B(T) and C(T) of a natural gas are now determined from the mole
fractions x and x (input data) and x , x and x (intermediate data) and the molar heating value H
CO H CH N CO CH
2 2 2
(see Figures B.1 and B.3).
16 © ISO 2006 – All rights reserved
ISO 12213-3:2006(E)
Figure B.3 — Flow diagram for compression factor calculation
B.3.1 Calculation of B(T)
The second virial coefficient B(T) is calculated from Equation (B.12) by the procedure described in B.2.2 for a
temperature
Tt=+ 273,15 (B.27)
B.3.2 Calculation of C(T)
The third virial coefficient for a natural gas at a temperature T is determined using the following equation:
3 222 2 2
C()T=x C+3xx C++3x x C 3xx C++3x x C 3xx C+6xx x C+
1 111 1 2 112 1 3 113 1 4 114 1 5 115 1 2 122 1 2 3 123
23 2 2 3 3
++33xx C x C+ x x C+3x x C+ x C+ x C (B.28)
1 3 133 2 222 2 3 223 2 3 233 3 333 4 444
The possible additional terms that are missing in Equation (B.28) have been found not to improve the
accuracy of the calculation if included and have therefore been set at zero.
ISO 12213-3:2006(E)
Furthermore, in Equation (B.28):
Cc=+cH +cH (B.29)
111 H0 H1 CH H2 CH
where c , c and c are second-degree polynomials as a function of temperature, viz:
H0 H1 H2
⎡⎤
Cc=+(0)c (1)T+c (2)T+c (0)+c (1)T+c (2)T H+
111 H0 H0 H0 H1 H1 H1 CH
⎣⎦
⎡⎤
++cc(0) (1)T+c (2)TH (B.30)
H2 H2 H2 CH
⎣⎦
as are C , C , C , C , C and C , viz:
222 333 444 115 223 233
Cc=+(0)c (1)T+c (2)T (B.31)
ijk ijk ijk ijk
The coefficients in Equations (B.30) and (B.31) are given in Table B.3.
Table B.3 — Numerical values of the coefficients c(0), c(1) and c(2) in the temperature expansion of the
third virial coefficient for pure gases and of the unlike-interaction virial coefficients
6 −2
(The units of C are m◊kmol when the temperature is in kelvins.)
ijk c(0) c(1) c(2)
−1 −3 −6
CH H0 − 3,024 88 × 10 1,958 61 × 10 − 3,163 02 × 10
−4 −6 −9
CH H1 6,464 22 × 10 − 4,228 76 × 10 6,881 57 × 10
−7 −9 −12
CH H2 − 3,328 05 × 10 2,231 60 × 10 − 3,677 13 × 10
−3 −5 −8
N 222 7,849 80 × 10 − 3,989 50 × 10 6,118 70 × 10
−3 −5 −8
CO 333 2,051 30 × 10 3,488 80 × 10 − 8,370 30 × 10
−3 −6 −9
H 444 1,047 11 × 10 − 3,648 87 × 10 4,670 95 × 10
CH + CH + N 112 y = 0,92 + 0,001 3 (T − 270)
CH + CH + CO 113 y = 0,92
CH + CH + H 114 y = 1,20
−3 −5 −8
CH + CH + CO 115 7,367 48 × 10 − 2,765 78 × 10 3,430 51 × 10
CH + N + N 122 y = 0,92 + 0,001 3 (T − 270)
2 2
CH + N + CO 123 y = 1,10
2 2
CH + CO + CO 133 y = 0,92
2 2
−3 −5 −8
N + N + CO 223 5,520 66 × 10 − 1,686 09 × 10 1,571 69 × 10
2 2 2
−3 −6 −8
N + CO + CO 233 3,587 83 × 10 8,066 74 × 10 − 3,257 98 × 10
2 2 2
The other unlike-interaction virial coefficients used are given by
Cy= CCC (B.32)
()
ijk ijk iii jjj kkk
where y is given by
ijk
yy== 0,92+ 0,0013(T− 270) (B.33)
112 122
yy== 0,92 (B.34)
113 133
18 © ISO 2006 – All rights reserved
ISO 12213-3:2006(E)
y = 1, 20 (B.35)
y = 1,10 (B.36)
Equation (B.32) shows that the temperature dependence of the unlike-interaction virial coefficients is
determined essentially by the temperature dependence of the third virial coefficients for the pure components.
B.4 Calculation of the compression factor and molar density
The very last stage in the calculation of the compression factor and the molar density is to solve Equations (1)
and (2) simultaneously for the given value of the pressure p. For the first approximation in the iteration using w,
ρ is given by
m
−1
ρ (0wR==) Tp+B (B.37)
m
where the second virial coefficient B is defined by Equation (B.12) for a temperature T (see Figure B.3). An
improved value ρ (w) is then given by
m
−12
⎡⎤
ρρ()wR=+Tp 1B (w−1)+Cρ (w−1) (B.38)
()
mm m
⎣⎦
where the third virial coefficient C for the mixture is defined by Equation (B.28) for a given temperature T. The
convergence criterion for the iteration using w is that the absolute difference between the calculated
−5
pressure p(w) given by Equation (B.39) and the given pressure p is less than 10 [see Equation (B.40)].
⎡⎤
p()wR=+Tρρ()w 1 B (w)+Cρ (w) (B.39)
mm m
⎣⎦
−5
pp−<()w 10 (B.40)
If this condition is not satisfied, then the current value for the molar density ρ (w) is used as the new value
m
ρ (w − 1) in Equation (B.38) and an improved value of the molar density ρ (w) is calculated.
m m
−5
However, if the left-hand side of Equation (B.40) is less than 10 , the iteration routine is ended, and ρ (w) is
m
the final molar density ρ . The compression factor is then given by
m
ZB=+1ρρ+C (B.41)
mm
NOTE The mass density can be calculated as follows:
ρ=dpρ (air)ZT pZT (B.42)
⎡⎤()
nnn n
⎣⎦
Z and Z being rounded to four places of decimals before being used in the density calculation.
n
Report the density to three significant figures.
ISO 12213-3:2006(E)
B.5 Consistency checks on the SGERG-88 method
The following tests, which provide partial consistency checks on the input data, shall be applied when carrying
out calculations by the SGERG method.
a) The input data shall satisfy the following condition:
dx> 0,55+−0,97 0,45x (B.43)
CO H
b) The intermediate calculated value for the mole fraction of nitrogen shall satisfy the following conditions:
− 0,01uux 0,5 (B.44)
N
xx+ u 0,5 (B.45)
NCO
c) Furthermore, the internal consistency of the input data for
...
Questions, Comments and Discussion
Ask us and Technical Secretary will try to provide an answer. You can facilitate discussion about the standard in here.
Loading comments...