SIST EN ISO 12213-2:2005
(Main)Natural gas - Calculation of compression factor - Part 2: Calculation using molar-composition analysis (ISO 12213-2:1997)
Natural gas - Calculation of compression factor - Part 2: Calculation using molar-composition analysis (ISO 12213-2:1997)
Erdgas - Berechnung von Realgasfaktoren - Teil 2: Berechnungen basierend auf einer molaren Gasanalyse als Eingangsgröße (ISO 12213-2:1997)
Gaz naturel - Calcul du facteur de compression - Partie 2: Calcul a partir de l'analyse de la composition molaire (ISO 12213-2:1997)
Zemeljski plin – Izračun kompresijskega faktorja – 2. del: Izračun na podlagi molarnih-kompozicijskih analiz (ISO 12213-2:1997)
General Information
Relations
Standards Content (Sample)
SLOVENSKI STANDARD
SIST EN ISO 12213-2:2005
01-julij-2005
=HPHOMVNLSOLQ±,]UDþXQNRPSUHVLMVNHJDIDNWRUMD±GHO ,]UDþXQQDSRGODJL
PRODUQLKNRPSR]LFLMVNLKDQDOL] ,62
Natural gas - Calculation of compression factor - Part 2: Calculation using molar-
composition analysis (ISO 12213-2:1997)
Erdgas - Berechnung von Realgasfaktoren - Teil 2: Berechnungen basierend auf einer
molaren Gasanalyse als Eingangsgröße (ISO 12213-2:1997)
Gaz naturel - Calcul du facteur de compression - Partie 2: Calcul a partir de l'analyse de
la composition molaire (ISO 12213-2:1997)
Ta slovenski standard je istoveten z: EN ISO 12213-2:2005
ICS:
75.060 Zemeljski plin Natural gas
SIST EN ISO 12213-2:2005 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
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SIST EN ISO 12213-2:2005
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SIST EN ISO 12213-2:2005
EUROPEAN STANDARD
EN ISO 12213-2
NORME EUROPÉENNE
EUROPÄISCHE NORM
May 2005
ICS 75.060
English version
Natural gas - Calculation of compression factor - Part 2:
Calculation using molar-composition analysis (ISO 12213-
2:1997)
Gaz naturel - Calcul du facteur de compression - Partie 2: Erdgas - Berechnung von Realgasfaktoren - Teil 2:
Calcul à partir de l'analyse de la composition molaire (ISO Berechnungen basierend auf einer molaren Gasanalyse als
12213-2:1997) Eingangsgröße (ISO 12213-2:1997)
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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Management Centre: rue de Stassart, 36 B-1050 Brussels
© 2005 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 12213-2:2005: E
worldwide for CEN national Members.
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SIST EN ISO 12213-2:2005
EN ISO 12213-2:2005 (E)
Foreword
The text of ISO 12213-2:1997 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 12213-2:2005 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 12213-2:1997 has been approved by CEN as EN ISO 12213-2:2005 without any
modifications.
2
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SIST EN ISO 12213-2:2005
INTERNATIONAL ISO
STANDARD 12213-2
First edition
1997-12-01
Natural gas — Calculation of compression
factor —
Part 2:
Calculation using molar-composition analysis
Gaz naturel — Calcul du facteur de compression —
Partie 2: Calcul par analyse de la composition molaire
A
Reference number
ISO 12213-2:1997(E)
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SIST EN ISO 12213-2:2005
ISO 12213-2:1997(E)
Contents Page
1 Scope . 1
2 Normative references . 1
3 Definitions . 1
4 Method of calculation . 2
4.1 Principle . 2
4.2 The AGA8-92DC 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 AGA8-92DC method . 9
C Example calculations . 15
D Pressure and temperature conversion factors . 16
E Performance over wider ranges of application . 17
F Subroutines in Fortran for the AGA8-92DC method . 21
G Bibliography . 28
© 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 12213-2:2005
©
ISO ISO 12213-2:1997(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 12213-2 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.
iii
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SIST EN ISO 12213-2:2005
©
INTERNATIONAL STANDARD ISO ISO 12213-2:1997(E)
Natural gas — Calculation of compression factor —
Part 2:
Calculation using molar-composition analysis
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 detailed composition
of the gas by mole fractions is known, together with the relevant pressures and temperatures.
The method is 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 %. It can be applied,
with greater uncertainty, to wider ranges of gas composition, pressure and temperature (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.
3 Definitions
All definitions relevant to the use of this part of ISO 12213 are given in part 1.
1
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ISO 12213-2:1997(E)
4 Method of calculation
4.1 Principle
The method recommended uses an equation based on the concept that pipeline quality natural gas may be
uniquely characterized for calculation of its volumetric properties by component analysis. This analysis, together
with the pressure and temperature, are used as input data for the method.
The method uses a detailed molar-composition analysis in which all constituents present in amounts exceeding a
mole fraction of 0,000 05 should be represented. Typically, this includes all alkane hydrocarbons up to about C or
7
C together with nitrogen, carbon dioxide and helium.
8
For other gases, additional components such as water vapour, hydrogen sulfide and ethylene need to be taken into
consideration (see reference [1] in annex G).
For manufactured gases, hydrogen and carbon monoxide are also likely to be significant components.
4.2 The AGA8-92DC equation
The compression factor is determined using the AGA8 detailed characterization equation (denoted hereafter as the
[1]
AGA8-92DC equation). This is an extended virial-type equation. The equation is described in AGA Report No. 8 . It
may be written as
18 58
kb k
nn n
* *
ZB=+1 rr− C + Cb −ckr r exp−cr . . . (1)
mr∑∑n n()nnnr r( nr)
nn==13 13
where
Z is the compression factor;
B is the second virial coefficient;
r is the molar density (moles per unit volume);
m
r is the reduced density;
r
b , c , k are constants (see table B.1);
n n n
*
are coefficients which are functions of temperature and composition.
C
n
The reduced density r is related to the molar density r by the equation
r m
3
rr=K . . . (2)
rm
where K is a mixture size parameter.
The molar density can be written as
r =pZRT . . . (3)
()
m
where
p is the absolute pressure;
R is the universal gas constant;
T is the absolute temperature.
*
Z is calculated as follows: first the values of B and C (n = 13 to 58) are calculated, using relationships given in
n
annex B. Equations (1) and (3) are then solved simultaneously for r and Z by a suitable numerical method (see
m
figure B.1).
2
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ISO 12213-2:1997(E)
4.3 Input variables
The input variables required for use with the AGA8-92DC equation are the absolute pressure, absolute temperature
and molar composition.
The composition is required, by mole fraction, of the following components: nitrogen, carbon dioxide, argon,
methane, ethane, propane, n-butane, methyl-2-propane (iso-butane), n-pentane, methyl-2-butane (iso-pentane),
hexanes, heptanes, octanes, nonanes, decanes, hydrogen, carbon monoxide, hydrogen sulfide, helium, oxygen
and water.
NOTE — If the mole fractions of the heptanes, octanes, nonanes and decanes are unknown, then use of a composite C
6+
fraction may be acceptable. The user should carry out a sensitivity analysis in order to test whether a particular approximation
of this type degrades the result.
All components with mole fractions greater than 0,000 05 shall be accounted for. Trace components (such as
ethylene) shall be treated as given in table 1.
If the composition is known by volume fractions, these shall be converted to mole fractions using the method given
in ISO 6976. The sum of all mole fractions shall be unity to within 0,000 1.
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
3 3
superior calorific value 30 MJ�m < H < 45 MJ�m
S
relative density 0,55 < d < 0,80
The mole fractions of the natural-gas components shall be within the following ranges:
methane 0,7 < x < 1,00
CH
4
nitrogen 0 < x < 0,20
N
2
carbon dioxide 0 < x < 0,20
CO
2
ethane 0 < x < 0,10
C H
2 6
propane 0 < x < 0,035
C H
3 8
butanes 0 < x < 0,015
C4H10
pentanes 0 < x < 0,005
C H
5 12
hexanes 0 < x < 0,001
C
6
heptanes 0 < x < 0,000 5
C
7
octanes plus 0 < x < 0,000 5
C
8+
higher hydrocarbons
hydrogen 0 < x < 0,10
H
2
carbon monoxide 0 < x < 0,03
CO
helium 0 < x < 0,005
He
water 0 < x < 0,000 15
H O
2
Any component for which x is less than 0,000 05 can be neglected.
i
Minor and trace components are listed in table 1.
3
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ISO 12213-2:1997(E)
Table 1 — Minor and trace components
Minor or trace component Assigned component
Oxygen oxygen
Argon argon
Hydrogen sulfide hydrogen sulfide
Ethylene, acetylene carbon dioxide
Propylene, propadiene propane
Butenes, butadienes n-butane
Neo-pentane, pentenes, benzene, cyclopentane n-pentane
All C -isomers, cyclohexane, ethylbenzene, xylenes n-hexane
6
All C -isomers, cycloheptane, toluene n-heptane
7
All C -isomers -octane
n
8
All C -isomers n-nonane
9
All C -isomers and all higher hydrocarbons n-decane
10
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.
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 < 65 MPa
temperature 225 K < T < 350 K
relative density 0,55 < d < 0,90
-3 -3
superior calorific value 20 MJ�m < H < 48 MJ�m
S
The allowable mole fractions of the major natural gas components are:
methane 0,50 < x < 1,00
CH
4
nitrogen 0 < 0,50
< x
N2
carbon dioxide 0 < x < 0,30
CO
2
ethane 0 < x < 0,20
C H
2 6
propane 0 < x < 0,05
C H
3 8
hydrogen 0 < x < 0,10
H
2
The limits for minor and trace gas components are as given in 4.4.1 for pipeline quality gas. For use of the method
outside these ranges, see annex E.
4.5 Uncertainty
4.5.1 Uncertainty for pipeline quality gas
The uncertainty of results for use on all pipeline quality gas within the limits described in 4.4.1 is – 0,1 % (for the
temperature range 263 K to 350 K and pressures up to 12 MPa) (see figure 1). For temperatures above 290 K and
at pressures up to 30 MPa the uncertainty of the result is also – 0,1 %.
For lower temperatures, the uncertainty of – 0,1 % is at least maintained for pressures up to about 10 MPa.
4
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ISO 12213-2:1997(E)
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 < 0,20, x < 0,10
N CO C H
2 2 2 6
-3 -3
and x < 0,10, and for 30 MJ�m < H < 45 MJ�m and 0,55 < d < 0,80)
H S
2
This uncertainty level has been determined by comparison with the GERG databank of measurements of the
[2], [3]
compression factor for natural gases . A detailed comparison was also made with the GRI PVT data on
[4], [5]
gravimetrically prepared simulated natural-gas mixtures .
The uncertainty of the measurements in both databanks used to test the method is of the order of – 0,1 %.
4.5.2 Uncertainty for wider ranges of application
The estimated uncertainties for calculations of compression factors beyond the limits of quality given in 4.4.1 are
discussed in annex E.
4.5.3 Impact of uncertainties of input variables
Listed in table 2 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 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.
5
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ISO 12213-2:1997(E)
Table 2 — Uncertainties of input variables
Input variable Absolute uncertainty
Absolute pressure – 0,02 MPa
Temperature – 0,15 K
Mole fraction of
inerts – 0,001
nitrogen – 0,001
carbon dioxide – 0,001
methane 0,001
–
ethane – 0,001
propane – 0,000 5
butanes – 0,000 3
pentanes plus higher hydrocarbons – 0,000 1
hydrogen and carbon monoxide 0,001
–
4.5.4 Reporting of results
Results for compression factor and molar density shall be reported to four and to five places of decimals,
respectively, together with the pressure and temperature values and the calculation method used (ISO 12213-2,
AGA8-92DC equation). For verification of calculation procedures, it is useful to carry extra digits.
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 12213-2:1997(E)
Annex A
(normative)
Symbols and units
Symbol Meaning Units
a Constant in table B.1 —
n
3 -1
B Second virial coefficient m �kmol
*
B Mixture interaction coefficient [equations (B.1) and (B.2)] —
nij
B Constant in table B.1 —
n
c Constant in table B.1 —
n
*
C Coefficients which are functions of temperature and composition —
n
E Characteristic energy parameter for ith component (table B.2) K
i
E Characteristic energy parameter for jth component (table B.2) K
j
Binary energy parameter for second virial coefficient K
E
ij
*
E Binary energy interaction parameter for second virial coefficient (table B.3) —
ij
F Mixture high-temperature parameter —
F High-temperature parameter for ith component (table B.2) —
i
F High-temperature parameter for jth component (table B.2) —
j
f Constant in table B.1 —
n
G Mixture orientation parameter —
G Orientation parameter for ith component (table B.2) —
i
G Orientation parameter for jth component (table B.2) —
j
G Binary orientation parameter —
ij
*
G Binary interaction parameter for orientation (table B.2) —
ij
g Constant in table B.1 —
n
3
H Superior calorific value MJ�m
S
3 1/3
K Size parameter (m /kmol)
3 1/3
K Size parameter for ith component (table B.2) (m /kmol)
i
3 1/3
K Size parameter for jth component (table B.2) (m /kmol)
j
K Binary interaction parameter for size (table B.3) —
ij
k Constant in table B.1 —
n
-1
M Molar mass kg�kmol
-1
M Molar mass of ith component kg�kmol
i
N Number of components in gas mixture
n An integer (from 1 to 58) —
p Absolute pressure MPa
Q Quadrupole parameter —
Q Quadrupole parameter for ith component —
i
Q Quadrupole parameter for jth component —
j
q Constant (table B.1) —
n
-1
Gas constant (= 0,008 314 510) MJ (kmol K)
R � �
S Dipole parameter for ith component (table B.2) —
i
S Dipole parameter for jth component (table B.2) —
j
s Constant (table B.1) —
n
7
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ISO 12213-2:1997(E)
Symbol Meaning Units
T Absolute temperature K
U Mixture energy parameter K
U Binary interaction parameter for mixture energy (table B.3) —
ij
u Constant in table B.1 —
n
W Association parameter for ith component (table B.2) —
i
W Association parameter for jth component (table B.2) —
j
w Constant (table B.1) —
n
x Mole fraction of ith component in gas mixture —
i
Mole fraction of th component in gas mixture —
x j
j
Z Compression factor —
-3
r Mass density kg�m
r Reduced density of gas —
r
-3
r Molar density kmol�m
m
8
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ISO
ISO 12213-2:1997(E)
Annex B
(normative)
Description of the AGA8-92DC method
B.1 General
For gas mixtures, the compression factor Z is calculated using the equations given in 4.2. This annex gives a
detailed description of the computations and the necessary numerical values. The description is based upon that
[1]
given in AGA Report No. 8 . A programme implementing this description is given in annex F, and as such
provides the correct solution. Other computational procedures are acceptable provided that they can be
demonstrated to yield identical numerical results (see annex C for examples).
B.2 Computer implementation of the AGA8-92DC method
B.2.1 Overview of the calculation procedure
I Input the absolute temperature T, absolute pressure p and mole fraction of each component x of the mixture.
i
NOTE — For pressure and temperature, values known in any other units will first have to be converted precisely to
values in megapascals and kelvins, respectively (see ISO 31-3 and ISO 31-4 and annex D for relevant conversion
factors).
*
II Compute the equation of state coefficients B and C (n = 13 to 58) that depend on T and x .
n i
III Solve iteratively for the molar density r , using the equation of state rearranged to give the pressure p.
m
IV Output the compression factor after the computed pressure from step III and the input pressure from step I
agree within a specified range of convergence (e.g. 1E-06).
Figure B.1 shows a flow diagram of these steps.
B.2.2 Details of the calculation procedure
Step I
Input the absolute temperature T, absolute pressure p and mole fraction x of each constituent in the natural-gas
i
mixture.
Step II
At the absolute temperature and the mole fractions of the natural gas (as input from step I), compute the
T x
i
*
composition- and temperature-dependent coefficients B and C (n = 13 to 58).
n
The second virial coefficient B is given by the following equations:
18 N N
32
u
−u n
n *
Ba= T xxBEKK . . . (B.1)
n ij ()ij
∑∑∑ nij ij
===
n1 i 1 j 1
f
g q s w
n
nn 12 12 nn
*
BG=+11−g QQ+−q FF +1−f SS+1−s WW+1−w . . . (B.2)
()( ) ()( )
nij ij n ij n()n ij n ij n
ij
9
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ISO 12213-2:1997(E)
Figure B.1 — AGA8-92DC equation — Calculation flow diagram
The binary parameters E and G are calculated using the following equations:
ij ij
12
*
EE= EE . . . (B.3)
ij ij()i j
*
GG=+G G2 . . . (B.4)
()
ij ij i j
* *
Note that all values of the binary interaction parameters E and G are 1,0 except for the values given in table B.3.
ij ij
*
The coefficients C (n = 13 to 58) are given by the equation:
n
g q f
n n n
* 2 uu−
nn
Ca=+G11−g Q+−q F+1−f U T . . . (B.5)
()()()
nn n n n
The mixture parameters U, G and Q are calculated using the following conformal solution mixing equations, where
in the double sums i ranges from 1 to N - 1 and, for each value of i, j ranges from i + 1 to N:
2
N−1
N N
52
52
5
5
Ux= E+−21xxU EE . . . (B.6)
i ij()()ij
∑∑i∑ ij
i==1 i=1 ji+1
N−1
N N
*
Gx=+G21xxG−G+G . . . (B.7)
()( )
∑ ii ∑ ∑ i j ij ij
i=1 i=1 ji=+1
10
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N
Qx= Q . . . (B.8)
∑ ii
i=1
N
2
Fx= F . . . (B.9)
i
∑i
i=1
* *
It should be noted that all values of the binary interaction parameters K , E , G and U are 1,0 except for the
ij ij ij ij
values given in table B.3. Also note that F is zero for all components except hydrogen, for which F(H ) = 1,0, and
i 2
that W is zero for all components except water, for which W(H O) = 1,0.
i 2
Step III
In the computation of the compression factor Z, the composition of the gas is known, the absolute temperature T of
the gas is known and the absolute pressure is known. The problem then is to compute the molar density r , using
m
the equation of state expression for the pressure p. For this purpose, the definition of the compression factor Z as
given in equation (1) (see 4.2) is substituted into equation (3) to obtain an equation for the pressure as given in
equation (B.10):
18 58
kb k
nn n
**
pR=+rrT1B−r C+ Cb−ckrr exp−cr . . . (B.10)
mmr∑nn∑()nnnrr( nr)
n= 13 n= 13
Equation (B.10) is solved using standard equation of state density search algorithms. Having obtained an equation
for the pressure p [equation (B.10)], the problem is then to search for the value of the molar density r that will yield
m
-6
the pressure that is within a preset limit (e.g. 1 · 10 ) equal to the input pressure.
The reduced density r is related to the molar density r by the mixture size parameter [see equation (2) in 4.2].
r m
The mixture size parameter K is calculated using the following equation:
2
N−1
N N
52
52
5
5
Kx= K+−21xxK KK . . . (B.11)
()()
∑∑ii∑ ij ij ij
i==1 i=1 ji+1
Note that in the summations the subscript i refers to the ith component in the gas mixture and the subscript j refers
to the jth component in the gas mixture. The quantity N is the number of components in the mixture. Thus, in the
single summation, i ranges over the integer values from 1 to N. For example, for a mixture of 12 components,
N = 12 and there would be 12 terms in the single sum. In the double summation, i ranges from 1 to N - 1 and, for
each value of i, j ranges from i + 1 to N. For example, for a mixture of 12 components, there would be 66 terms in
the double summation if all values of K differed from 1,0. However, because many of the values of K are 1,0, the
ij ij
number of non-zero terms in the double summation is small for many natural-gas mixtures. Note that all values of
K are 1,0 except for the values given in table B.3.
ij
Step IV
Once the molar density r has been obtained in step III, the compression factor is calculated in step IV using the
m
pressure, temperature, molar density and gas constant:
Zp= rRT . . . (B.12)
()
m
NOTE — The density r (mass per unit volume) can be calculated as follows:
r = Mr . . . (B.13)
m
11
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SIST EN ISO 12213-2:2005
©
ISO
ISO 12213-2:1997(E)
where M is calculated from the equation:
N
Mx= M . . . (B.14)
ii
∑
i=1
Report the density to three places of decimals.
Table B.1 — Equation of state parameters
na b c k u g q f s w
n n n n n n n n n n
1 0,153 832 600 1 0 0 0,0 0 0 0 0 0
2 1,341 953 000 1 0 0 0,5 0 0 0 0 0
3 - 2,998 583 000 1 0 0 1,0 0 0 0 0 0
4 - 0,048 312 280 1 0 0 3,5 0 0 0 0 0
5 0,375 796 500 1 0 0 - 0,5 1 0 0 0 0
6 - 1,589 575 000 1 0 0 4,5 1 0 0 0 0
7 - 0,053 588 470 1 0 0 0,5 0 1 0 0 0
8 0,886 594 630 1 0 0 7,5 0 0 0 1 0
9 0,710 237 040 1 0 0 9,5 0 0 0 1 0
-
10 - 1,471 722 000 1 0 0 6,0 0 0 0 0 1
11 1,321 850 350 1 0 0 12,0 0 0 0 0 1
12 - 0,786 659 250 1 0 0 12,5 0 0 0 0 1
-9
13 2,291 290 · 10 113 - 6,0 0 0 1 0 0
14 0,157 672 400 1 1 2 2,0 0 0 0 0 0
15 - 0,436 386 400 1 1 2 3,0 0 0 0 0 0
16 - 0,044 081 590 1 1 2 2,0 0 1 0 0 0
17 - 0,003 433 888 1 1 4 2,0 0 0 0 0 0
18 0,032 059 050 1 1 4 11,0 0 0 0 0 0
19 0,024 873 550 2 0 0 - 0,5 0 0 0 0 0
20 0,073 322 790 2 0 0 0,5 0 0 0 0 0
21 - 0,001 600 573 2 1 2 0,0 0 0 0 0 0
22 0,642 470 600 2 1 2 4,0 0 0 0 0 0
23 - 0,416 260 100 2 1 2 6,0 0 0 0 0 0
24 - 0,066 899 570 2 1 4 21,0 0 0 0 0 0
25 0,279 179 500 2 1 4 23,0 1 0 0 0 0
26 - 0,696 605 100 2 1 4 22,0 0 1 0 0 0
27 - 0,002 860 589 2 1 4 - 1,0 00 10 0
28 - 0,008 098 836 3 0 0 - 0,5 0 1 0 0 0
29 3,150 547 000 3 1 1 7,0 1 0 0 0 0
30 0,007 224 479 3 1 1 - 1,0 0 0 1 0 0
31 - 0,705 752 900 3 1 2 6,0 0 0 0 0 0
32 0,534 979 200 3 1 2 4,0 1 0 0 0 0
33 - 0,079 314 910 3 1 3 1,0 1 0 0 0 0
34 1,418 465 000 3 1 3 9,0 1 0 0 0 0
-
-17
35 - 5,999 05 · 10 314 - 13,0 0 0 1 0 0
36 0,105 840 200 3 1 4 21,0 0 0 0 0 0
37 0,034 317 290 3 1 4 8,0 0 1 0 0 0
38 - 0,007 022 847 4 0 0 - 0,5 0 0 0 0 0
39 0,024 955 870 4 0 0 0,0 0 0 0 0 0
40 0,042 968 180 4 1 2 2,0 0 0 0 0 0
41 0,746 545 300 4 1 2 7,0 0 0 0 0 0
42 - 0,291 961 300 4 1 2 9,0 0 1 0 0 0
43 7,294 616 000 4 1 4 22,0 0 0 0 0 0
44 - 9,936 757 000 4 1 4 23,0 0 0 0 0 0
45 - 0,005 399 808 5 0 0 1,0 0 0 0 0 0
46 - 0,243 256 700 5 1 2 9,0 0 0 0 0 0
47 0,049 870 160 5 1 2 3,0 0 1 0 0 0
48 0,003 733 797 5 1 4 8,0 0 0 0 0 0
49 1,874 951 000 5 1 4 23,0 0 1 0 0 0
50 0,002 168 144 6 0 0 1,5 0 0 0 0 0
51 - 0,658 716 400 6 1 2 5,0 1 0 0 0 0
52 0,000 205 518
...
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