SIST EN ISO 12213-3:2005
(Main)Natural gas - Calculation of compression factor - Part 3: Calculation using physical properties (ISO 12213-3:1997)
Natural gas - Calculation of compression factor - Part 3: Calculation using physical properties (ISO 12213-3:1997)
Erdgas - Berechnung von Realgasfaktoren - Teil 3: Berechnungen basierend auf physikalischen Stoffeigenschaften als Eingangsgrößen (ISO 12213-3:1997)
Gaz naturel - Calcul du facteur de compression - Partie 3: Calcul a partir des caractéristiques physiques (ISO 12213-3:1997)
Zemeljski plin – Izračun kompresijskega faktorja – 3. del: Izračun na podlagi fizikalnih lastnosti (ISO 12213-3:1997)
General Information
Relations
Standards Content (Sample)
SLOVENSKI STANDARD
SIST EN ISO 12213-3:2005
01-julij-2005
=HPHOMVNLSOLQ±,]UDþXQNRPSUHVLMVNHJDIDNWRUMD±GHO ,]UDþXQQDSRGODJL
IL]LNDOQLKODVWQRVWL ,62
Natural gas - Calculation of compression factor - Part 3: Calculation using physical
properties (ISO 12213-3:1997)
Erdgas - Berechnung von Realgasfaktoren - Teil 3: Berechnungen basierend auf
physikalischen Stoffeigenschaften als Eingangsgrößen (ISO 12213-3:1997)
Gaz naturel - Calcul du facteur de compression - Partie 3: Calcul a partir des
caractéristiques physiques (ISO 12213-3:1997)
Ta slovenski standard je istoveten z: EN ISO 12213-3:2005
ICS:
75.060 Zemeljski plin Natural gas
SIST EN ISO 12213-3:2005 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
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SIST EN ISO 12213-3:2005
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SIST EN ISO 12213-3:2005
EUROPEAN STANDARD
EN ISO 12213-3
NORME EUROPÉENNE
EUROPÄISCHE NORM
May 2005
ICS 75.060
English version
Natural gas - Calculation of compression factor - Part 3:
Calculation using physical properties (ISO 12213-3:1997)
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
3:1997) Stoffeigenschaften als Eingangsgrößen (ISO 12213-
3:1997)
This European Standard was approved by CEN on 17 April 2005.
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 Central Secretariat 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 Central Secretariat has the same status as the official
versions.
CEN members are the national standards bodies of Austria, Belgium, Cyprus, Czech Republic, Denmark, Estonia, Finland, France,
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Slovenia, Spain, Sweden, Switzerland and United Kingdom.
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© 2005 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 12213-3:2005: E
worldwide for CEN national Members.
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SIST EN ISO 12213-3:2005
EN ISO 12213-3:2005 (E)
Foreword
The text of ISO 12213-3:1997 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 12213-3:2005 by CMC.
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 November 2005, and conflicting national
standards shall be withdrawn at the latest by November 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,
Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary,
Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland,
Portugal, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom.
Endorsement notice
The text of ISO 12213-3:1997 has been approved by CEN as EN ISO 12213-3:2005 without any
modifications.
2
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SIST EN ISO 12213-3:2005
INTERNATIONAL ISO
STANDARD 12213-3
First edition
1997-12-01
Natural gas — Calculation of compression
factor —
Part 3:
Calculation using physical properties
Gaz naturel — Calcul du facteur de compression —
Partie 3: Calcul au moyen des caractéristiques physiques
A
Reference number
ISO 12213-3:1997(E)
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SIST EN ISO 12213-3:2005
ISO 12213-3:1997(E)
Contents Page
1 Scope . 1
2 Normative references . 1
3 Definitions . 2
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 . 4
5 Suppliers of computer programmes . 6
Annexes
A Symbols and units . 7
B Description of the SGERG-88 method . 9
C Example calculations . 18
D Conversion factors . 19
E Performance over wider ranges of application . 22
F Subroutine SGERG.FOR in Fortran . 26
G Bibliography . 30
© ISO 1997
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 the publisher.
International Organization for Standardization
Case postale 56 • CH-1211 Genève 20 • Switzerland
Internet central@iso.ch
X.400 c=ch; a=400net; p=iso; o=isocs; s=central
Printed in Switzerland
ii
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SIST EN ISO 12213-3:2005
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ISO ISO 12213-3:1997(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.
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.
International Standard ISO 12213-3 was prepared by Technical Committee
ISO/TC 193, Natural gas, Subcommittee SC 1, Analysis of natural gas.
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
Annexes A to D form an integral part of this part of ISO 12213. Annexes E
to G are for information only.
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SIST EN ISO 12213-3:2005
©
INTERNATIONAL STANDARD ISO ISO 12213-3:1997(E)
Natural gas — Calculation of compression factor —
Part 3:
Calculation using physical properties
1 Scope
This International Standard 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 E).
More detail concerning the scope and field of application of the method is given in part 1 of this International
Standard.
2 Normative references
The following standards contain provisions which, through reference in this text, constitute provisions of this part of
ISO 12213. At the time of publication, the editions indicated were valid. All standards are subject to revision, and
parties to agreements based on this part of ISO 12213 are encouraged to investigate the possibility of applying the
most recent editions of the standards indicated below. Members of IEC and ISO maintain registers of currently valid
International Standards.
ISO 31-3:1992, Quantities and units — Part 3: Mechanics.
ISO 31-4:1992, Quantities and units — Part 4: Heat.
ISO 6976:1995, Natural gas — Calculation of calorific values, density, relative density and Wobbe index from
composition.
ISO 12213-1:1997, Natural gas — Calculation of compression factor — Part 1: Introduction and guidelines.
1
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ISO 12213-3:1997(E)
3 Definitions
All definitions relevant to the use of this part of ISO 12213 are given in part 1.
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 equation
[1], [2], [3]
for natural gases . The standard GERG 88 virial equation is derived from the master GERG 88
[4]
(MGERG-88) virial equation, which is a method of calculation based on a molar-composition analysis .
The SGERG-88 virial equation from which the compression factor Z is calculated may be written as
2
ZB=+1 rr+C . . . (1)
mm
where
B and C are functions of the input data comprising the superior calorific value H , the relative density d, the
S
contents of both inert and combustible non-hydrocarbon components of the gas mixture (CO and H )
2 2
and the temperature T;
r is the molar density given by
m
r =pZ()RT . . . (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 needed. Therefore, the calculation of Z
CH
uses
Z = f ( , , , , , , , ) . . . (4)
p T H x x x x x
2 CH CH N2 CO2 H2 CO
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 ( 0,001), then set = 0. The natural-gas mixture
x < x
H2 H2
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.
2
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ISO 12213-3:1997(E)
Secondly, once this composition is known, B and C may be found using relationships also given in annex B.
In the third step, equations (1) and (2) are solved simultaneously for r and Z by a suitable numerical method.
m
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 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 virial equation:
x , H , d and x (set B)
N S H
2 2
x , x , d and x (set C)
N2 CO2 H2
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 < p < 12 MPa
temperature 263 K < T < 338 K
mole fraction of carbon dioxide 0 < x < 0,20
CO
2
mole fraction of hydrogen 0 < x < 0,10
H
2
-3 -3
superior calorific value 30 MJ�m < H < 45 MJ�m
S
relative density 0,55 < d < 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:
methane 0,7 < x < 1,0
CH
4
nitrogen 0 < x < 0,20
N
2
ethane 0 < x < 0,10
C H
2 6
propane 0 < x < 0,035
C H
3 8
butanes 0 < x < 0,015
C H
4 10
3
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pentanes 0 < x < 0,005
C H
5 12
hexanes 0 < x < 0,001
C
6
heptanes 0 < x < 0,000 5
C7
octanes plus higher hydrocarbons 0 < x < 0,000 5
C
8+
carbon monoxide 0 < x < 0,03
CO
helium 0 < x < 0,005
He
water 0 < x < 0,000 15
H O
2
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, 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 < p < 12 MPa
temperature 263 K < T < 338 K
< 0,30
mole fraction of carbon dioxide 0 < x
CO2
mole fraction of hydrogen 0 < x < 0,10
H
2
- -
3 3
superior calorific value 20 MJ�m < H < 48 MJ�m
S
relative density 0,55 < d < 0,90
The allowable mole fractions of other major natural-gas components are extended to:
methane 0,5 < x < 1,0
CH
4
nitrogen 0 < x < 0,50
N
2
ethane 0 < x < 0,20
C H
2 6
propane 0 < x < 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.
4.5 Uncertainty
4.5.1 Uncertainty for pipeline quality gas
The uncertainty in the prediction of the compression factor DZ (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 x < 0,20,
N
2
-3 -3
x < 0,09, x < 0,10 and x < 0,10, and for 30 MJ�m < H < 45 MJ�m and 0,55 < d < 0,80, (see
CO C H H S
2 2 6 2
figure 1).
For gases with a CO content exceeding 0,09, the uncertainty of – 0,1 % is maintained for pressures up to 6 MPa
2
and for temperatures between 263 K and 338 K. This uncertainty level is determined by comparison with the GERG
[5], [6]
databank on measurements of the compression factor for natural gases and with the Gas Research Institute
[9]
data .
4
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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 < 0,20; x < 0,09; x < 0,10 and x < 0,10,
N CO C H H
2 2 2 6 2
-3 -3
and for 30 MJ�m < H < 45 MJ�m and 0,55 < d < 0,80)
S
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 E.
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.
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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 Suppliers of computer programmes
It is planned to make software available which implements this International Standard. Users are invited to contact
their ISO member body or ISO Central Secretariat to enquire about the availability of such software.
6
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ISO 12213-3:1997(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)]
11
3 -1
b (0) m �kmol
H0
3 -1 -1
(1) Terms in the temperature expansion of [equation (B.21)] m �kmol �K
b b
H0 H0
3 -1 -2
b (2) m �kmol �K
H0
3 -1
b (0) m �MJ
H1
3 -1 -1
b (1) Terms in the temperature expansion of b [equation (B.21)] m �MJ �K
H1 H1
3 -1 -2
b (2) m �MJ �K
H1
3 -2
b (0) m �kmol�MJ
H2
3 -2 -1
b (1) Terms in the temperature expansion of b [equation (B.21)]
m �kmol�MJ �K
H2 H2
3 - -
b (2) 2 2
H2 m �kmol�MJ �K
3 -1
b (0) m �kmol
ij
3 -1 -1
m �kmol �K
b (1) Terms in the temperature expansion of b [equation (B.22)]
ij ij
3 -1 -2
m �kmol �K
b (2)
ij
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 C m �kmol
H0 CH 111
[equation (B.29)]
6 -1 -1
c First-order (linear) term in the molar heating value (H ) expansion of C m �kmol �MJ
H1 CH 111
[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)]
111
6 -2
c (0) m �kmol
H0
6 -2 -1
(1) Terms in the temperature expansion of [equation (B.30)] m �kmol �K
c c
H0 H0
6 -2 -2
c (2) m �kmol �K
H0
6 -1 -1
c (0) m �kmol �MJ
H1
6 -1 -1 -1
c (1) Terms in the temperature expansion of c [equation (B.30)] m �kmol �MJ �K
H1 H1
6 -1 -1 -2
c (2) m �kmol �MJ �K
H1
6 -2
c (0) m �MJ
H2
6 -2 -1
c (1) Terms in the temperature expansion of c [equation (B.30)] m �MJ �K
H2 H2
6 -2 -2
c (2) m �MJ �K
H2
6 -2
c (0) m �kmol
ijk
6 -2 -1
c (1) Terms in the temperature expansion of c [equation (B.31)] m �kmol �K
ijk ij
6 -2 -2
m �kmol �K
c (2)
ijk
6 -2
C Third virial coefficient [equation (1)] m �kmol
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Symbol Meaning Units
6 -2
C Third virial coefficient for ternary interaction between components i, j and k m �kmol
ijk
[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
Molar volume (= 1/)m�kmol
V r
m m
x Mole fraction of a component —
y —
Combination rule parameters for the binary unlike-interaction virial coefficients
B and B (table B.1) and the ternary unlike-interaction virial coefficient C
12 13 ijk
[equation (B.32)]
Z Compression factor —
-3
r Mass density [equations (B.8) and (B.42)] kg�m
-1 -3
r Molar density (= V ) kmol�m
m m
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
2
H For hydrogen
2
N For nitrogen
2
Additional qualifiers
(air) For dry air of standard composition [equation (B.1)]
(D) For special value of r 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)
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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.
Figure B.1 — Flow diagram for standard GERG-88 calculation method
(x = mole fraction of component i)
i
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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
3
dioxide and hydrogen. If the values of the first three parameters are in any units other than bar, °C and MJ/m , they
3
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
2
carbon monoxide x
CO
Molar heating value of the equivalent hydrocarbon H
CH
Molar mass of the equivalent hydrocarbon M
CH
Second virial coefficient (T = 273,15 K) B
n n
Molar density at normal conditions r
m,n
Mass density at normal conditions r
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 , r , r ) are determined from equations (B.1) to
CH N CO CH CH n m,n n
2
(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.
rr= d (air) . . . (B.1)
nn
xx= 0,096 4 . . . (B.2)
CO H2
Vi()d =RT p . . . (B.3)
m,n n n
−1
r ()vV=+(id) B (v) . . . (B.4)
m,n[]m,n n
10
---------------------- Page: 18 ----------------------
SIST EN ISO 12213-3:2005
©
ISO
ISO 12213-3:1997(E)
Figure B.2 — Flow diagram for computing intermediate data by iteration
11
---------------------- Page: 19 ----------------------
SIST EN ISO 12213-3:2005
©
ISO
ISO 12213-3:1997(E)
Mu()=− 2,709 328+ 0,021062 199Hu( − 1) . . . (B.5)
CH CH
xu()=−H H (u11)r (v)− x H+x H H (u− . . . (B.6)
[]m,n()
CH SCH []H H CO CO CH
22
xu()=−1 x ()u −x −x −x . . . (B.7)
N CH CO H CO
2 2 2
rr()u=+x ()uM ()u x ()uM (v)+ x M+ x M+ x Mr (v) . . . (B.8)
n[]CH CH NN m,n()CO CO HH CO CO m,n
22 22 22
Table B.1 — Values of the constants used in equation (B.1)
(adjusted to conform with the molar masses and molar calorific values in ISO 6976:1975)
-1
H = 285,83 MJ�kmol
H
2
-1
H = 282,98 MJ�kmol
CO
-1
N = 28,013 5 kg�kmol
N
2
-1
M = 44,010 kg�kmol
CO
2
-1
M = 2,015 9 kg�kmol
H
2
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
r (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 ( ) and the known density (either measured directly or determined from the
r u
n
-6
relative density) of the gas at normal conditions r is less than 10 , i.e.
n
−6
rr−<()u 10 . . . (B.9)
nn
If this condition is not satisfied, then an improved value of the molar heating value H (u), for use in equations (B.5)
CH
to (B.8),
...
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