kSIST FprEN ISO 17507-2:2025

SLOVENSKI STANDARD
oSIST prEN ISO 17507-2:2024
01-december-2024
[Not translated]
Natural gas - Calculation of methane number of gaseous fuels for reciprocating internal
combustion engines - Part 2: PKI method (ISO/DIS 17507-2:2024)
Erdgas - Berechnung der Methanzahl von gasförmigen Kraftstoffen für
Verbrennungsmotoren - Teil 2: PKI-Verfahren (ISO/DIS 17507-2:2024)
Gaz naturel - Calcul de l'indice de méthane des combustibles gazeux pour les moteurs
alternatifs à combustion interne - Partie 2: Méthode PKI (ISO/DIS 17507-2:2024)
Ta slovenski standard je istoveten z: prEN ISO 17507-2
ICS:
75.060 Zemeljski plin Natural gas
oSIST prEN ISO 17507-2:2024 en,fr,de
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

oSIST prEN ISO 17507-2:2024
oSIST prEN ISO 17507-2:2024
DRAFT
International
Standard
ISO/DIS 17507-2
ISO/TC 193
Natural gas — Calculation of
Secretariat: NEN
methane number of gaseous
Voting begins on:
fuels for reciprocating internal
2024-10-17
combustion engines —
Voting terminates on:
2025-01-09
Part 2:
PKI method
ICS: 75.060
THIS DOCUMENT IS A DRAFT CIRCULATED
FOR COMMENTS AND APPROVAL. IT
IS THEREFORE SUBJECT TO CHANGE
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Reference number
ISO/DIS 17507-2:2024(en)
oSIST prEN ISO 17507-2:2024
DRAFT
ISO/DIS 17507-2:2024(en)
International
Standard
ISO/DIS 17507-2
ISO/TC 193
Natural gas — Calculation of
Secretariat: NEN
methane number of gaseous
Voting begins on:
fuels for reciprocating internal
combustion engines —
Voting terminates on:
Part 2:
PKI method
ICS: 75.060
THIS DOCUMENT IS A DRAFT CIRCULATED
FOR COMMENTS AND APPROVAL. IT
IS THEREFORE SUBJECT TO CHANGE
AND MAY NOT BE REFERRED TO AS AN
INTERNATIONAL STANDARD UNTIL
PUBLISHED AS SUCH.
This document is circulated as received from the committee secretariat.
IN ADDITION TO THEIR EVALUATION AS
BEING ACCEPTABLE FOR INDUSTRIAL,
© ISO 2024
TECHNOLOGICAL, COMMERCIAL AND
USER PURPOSES, DRAFT INTERNATIONAL
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
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Published in Switzerland Reference number
ISO/DIS 17507-2:2024(en)
ii
oSIST prEN ISO 17507-2:2024
ISO/DIS 17507-2:2024(en)
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols and abbreviated terms. 2
5 MN method . 2
PKI
5.1 Introduction .2
5.2 Applicability .2
5.2.1 Standard gaseous fuel composition range .2
5.2.2 Handling of other gaseous fuel components .3
5.3 Methodology to calculate the MN .4
PKI
5.4 Expression of results . .5
5.5 Uncertainty error and bias .5
6 Example calculations . 5
6.1 Example calculation 1 .5
6.2 Example calculation 2 .6
Annex A (normative) Listing of coefficients used in Formula (1) and Formula (4) . 9
Annex B (informative) PKI and MN values for selected gaseous fuel compositions .13
PKI
Annex C (informative) Tools for users of the MN method .15
PKI
Annex D (normative) Uncertainty error and bias .16
Annex E (informative) Natural gas-based fuels for reciprocating internal combustion engines .18
Annex F (informative) Basis of the PKI method . 19
Bibliography .22

iii
oSIST prEN ISO 17507-2:2024
ISO/DIS 17507-2:2024(en)
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.
The procedures used to develop this document and those intended for its further maintenance are described
in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the different types
of ISO documents should be noted. This document was drafted in accordance with the editorial rules of the
ISO/IEC Directives, Part 2 (see www.iso.org/directives).
ISO draws attention to the possibility that the implementation of this document may involve the use of (a)
patent(s). ISO takes no position concerning the evidence, validity or applicability of any claimed patent
rights in respect thereof. As of the date of publication of this document, ISO [had/had not] received notice of
(a) patent(s) which may be required to implement this document. However, implementers are cautioned that
this may not represent the latest information, which may be obtained from the patent database available at
www.iso.org/patents. ISO shall not be held responsible for identifying any or all such patent rights.
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and expressions
related to conformity assessment, as well as information about ISO's adherence to the World Trade
Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 193, Natural gas.
A list of all parts in the ISO 17507 series can be found on the ISO website.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www.iso.org/members.html.

iv
oSIST prEN ISO 17507-2:2024
ISO/DIS 17507-2:2024(en)
Introduction
The globalization of the natural gas market and the drive towards sustainability are increasing the diversity
of the supply of gases to the natural gas infrastructure. For example, the introduction of regasified LNG
can result in higher fractions of non-methane hydrocarbons in the natural gas grid than the traditionally
distributed pipeline gases for which these hydrocarbons have been removed during processing. Also, the
drive towards the introduction of sustainable gaseous fuels such as hydrogen and gases derived from
biomass results in the introduction of “new” gas compositions, containing components that do not occur
in the traditional natural gas supply. Consequently, the increasing variations in gas composition affect
the so-called knock resistance of the gas when used as a fuel which can affect the operational integrity of
reciprocating internal combustion engines.
For the efficient and safe operation of gas engines, it is of great importance to characterize the knock
resistance of gaseous fuels accurately. Engine knock is caused by autoignition of unburned fuel mixture ahead
of this mixture being consumed by the propagating flame. Mild engine knock increases pollutant emissions
accompanied by gradual build-up of component damage and complete engine failure if not counteracted.
Severe knock causes structural damage to critical engine parts, quickly leading to catastrophic engine
failure. To ensure that gas engines are matched with the expected variations in fuel composition, the knock
resistance of the fuel is to be characterized, and subsequently specified, unambiguously.
Traditional methods for characterizing the knock resistance of gaseous fuels, such as the methane number
method developed by AVL in the 1960s, relate the knock propensity of a given fuel with that of an equivalent
[1] [2] [3]
methane/hydrogen mixture using a standardized test engine , and. Several other methane number
methods have since been developed, sometimes based on the approach and/or data from the original
experimental work performed by AVL.
In recognition of the need for standardizing a method for characterizing the knock resistance of gaseous
fuels, several existing methods for calculating a methane number have been considered including the PKI
[4]
method which is described in this document. ISO 17507-1 describes the MNc method.
Methods to calculate a methane number are based on the input of the gas composition under investigation.
While methods may be fundamentally different in their development approach, the methods should ideally
produce similar methane numbers for the range of gas compositions they are valid for. Yet, differences in
outcome can be observed. Engine manufacturers typically determine the calculation method to be used
when specifying a methane number value for their engines as part of their application and warranty
statements. In all cases, when specifying a methane number based on either method, or any other method,
the method used should be noted.
The PKI method has been developed by DNV in a consortium of engine Original Equipment Manufacturers
(OEMs) and natural gas fuel suppliers. The method is based on the physics and chemistry of the air-fuel
mixture during the compression and combustion phases of the engine working cycle that determine engine
knock, using an experimentally verified engine combustion model.
The PKI method uses two polynomial functions to compute the methane number from the gaseous fuel
composition input. The development and experimental verification of the PKI method is documented in a
[5-17]
series of publications. A more detailed history of the PKI method can be found in Annex F.
A version of the PKI method dedicated to LNG fuels is currently described in ANNEX A of ISO 23306
[18] [19]
“Specification of liquefied natural gas as a fuel for marine applications” and .

v
oSIST prEN ISO 17507-2:2024
oSIST prEN ISO 17507-2:2024
DRAFT International Standard ISO/DIS 17507-2:2024(en)
Natural gas — Calculation of methane number of gaseous
fuels for reciprocating internal combustion engines —
Part 2:
PKI method
1 Scope
The methane number of a gas quantifies the knock propensity of that gas when used as a fuel in a
reciprocating internal combustion engine. The higher the methane number, the more knock resistant the
gas is, and vice versa.
This document defines the PKI method for the calculation of the methane number of a gaseous fuel, using the
composition of the gas as sole input for the calculation.
This document applies to natural gas (and biomethane) and their admixtures with hydrogen; see Clause 5.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content constitutes
requirements 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 14532:2014, Natural gas — Vocabulary
ISO 14912, Gas analysis — Conversion of gas mixture composition data
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 14532 and the following apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
3.1
methane number
MN
numerical rating indicating the knock resistance of a gaseous fuel
Note 1 to entry: It is analogous to the octane number for petrol. The methane number is the volume fraction expressed
as percentage of methane in a methane-hydrogen mixture, that in a test engine under standard conditions has the
same knock resistance as the gaseous fuel to be examined.
[SOURCE: ISO 14532:2014, 2.6.6.1]

oSIST prEN ISO 17507-2:2024
ISO/DIS 17507-2:2024(en)
3.2
PKI methane number
MN
PKI
calculation of a numerical rating index indicating the knock resistance of a gaseous fuel according to
ISO 17507-2
Note 1 to entry: This analytical estimate of a methane number is based on using mole fraction gaseous fuel composition
as input.
4 Symbols and abbreviated terms
MN Methane Number
PKI Propane Knock Index
MN PKI Methane Number
PKI
5 MN method
PKI
5.1 Introduction
The methane number of a gaseous fuel is calculated from its composition according to several different methods,
all of which can give different results. The PKI method is in use by engine OEMs, gaseous fuel suppliers, engine
operators, consulting engineers and engine control and gas analyser equipment OEMs, and has been adopted
[19]
in ISO 23306 . When referring to a methane number value, the method used should be noted.
The PKI method described in this document has been developed for a range of gaseous fuel compositions
exceeding the typical composition range of natural gas-based fuels used in reciprocating internal combustion
engines shown in Table E.1 .
The PKI method thus can be used for the calculation of the methane number of any gaseous engine fuel as
long as the gas composition input ranges, shown in Table 1, and further boundary conditions of this method
are adhered to. The boundary conditions for the PKI method are set out in this document.
The method is based on gaseous fuel compositions in mole fraction, expressed as a percentage. If the gas
composition is available either as volume fraction or as mass fraction, conversion to mole fraction shall be
performed using the methods in ISO 14912.
Calculation of the MN from the gas composition involves two polynomial functions, as described in 5.3.
PKI
Numerical examples are provided to enable software developers to validate implementations of the method
described in this document.
5.2 Applicability
5.2.1 Standard gaseous fuel composition range
The PKI method described in this document has been developed for and is applicable to all reciprocating
internal combustion engines using a gaseous fuel.
In general, the use of any method for calculating the methane number of a gaseous fuel requires careful
consideration and/or consultation with specialist industry parties such as engine suppliers, fuel suppliers
and consulting firms.
The PKI method described in this document is applicable to gaseous fuels comprising the following
components: methane, ethane, propane, n-butane, i-butane, n-pentane, i-pentane, neo-pentane, hexanes,
hydrogen, carbon monoxide, carbon dioxide, nitrogen and hydrogen sulfide.
Upper and lower limits for gaseous fuels applied to this method are shown in Table 1.

oSIST prEN ISO 17507-2:2024
ISO/DIS 17507-2:2024(en)
Table 1 — Upper and lower limits of gaseous fuel components
for the PKI method
Amount of substance
Mole fraction
Component
%
Methane 65 – 100
Ethane 0 – 20
Propane 0 – 20
a
n-Butane 0 – 5
a
i-Butane 0 – 5
a
n-Pentane 0 – 2
a
i-Pentane 0 – 2
a
neo-Pentane 0 – 2
+ b
Hexanes 0 – 1,5
Hydrogen 0 – 35
Carbon monoxide 0 – 10
Carbon dioxide 0 – 20
Nitrogen 0 – 20
Hydrogen sulfide 0 – 0,5
a
The PKI method differentiates between the isomers of butane and pentane in
recognition of their difference in knock propensity.
b
The PKI method treats the sum of hexanes and higher hydrocarbons including their
+
isomers (listed as hexanes ) as n-hexane.
Gas composition analyses may comprise of (non-)hydrocarbon components not listed as valid gas input
components for the PKI method as per Table 1. To provide guidance towards the correct use of and optimum
results from the PKI method, instructions for the handling of a selection of such non-listed gas components
is given in 5.2.2.
5.2.2 Handling of other gaseous fuel components
5.2.2.1 Oxygen and water vapour
Any oxygen and water vapour present in the gaseous fuel under investigation shall be ignored, meaning
their fractions shall be set to equal zero (0). The resulting gas composition shall be normalized to obtain a
sum of 100 %, or unity in the case of using fractions.
5.2.2.2 Argon and helium
Any argon or helium present in the gaseous fuel under investigation shall be assigned to the fraction of
nitrogen, meaning their fractions shall be added to that of nitrogen. This assignment does not affect the sum
total of the resulting gas composition. If needed, the resulting gas composition shall be normalized to obtain
a sum of 100 %, or unity in the case of using fractions.
5.2.2.3 Other non-listed gaseous fuel components
Any component present in the gaseous fuel under investigation not listed as valid gas input component for
the PKI method as per Table 1 and not listed in 5.2.2.1 or 5.2.2.2, shall be ignored, meaning their fractions
shall be set to equal zero (0). The resulting gas composition shall be normalized to obtain a sum of 100 %, or
unity in the case of using fractions.

oSIST prEN ISO 17507-2:2024
ISO/DIS 17507-2:2024(en)
5.3 Methodology to calculate the MN
PKI
The MN of the gaseous fuel under investigation is calculated from its composition in two steps:
PKI
1. calculation of the PKI, based on the gas composition;
2. calculation of the MN , based on the PKI calculated in Step 1.
PKI
Step 1: Calculation of the PKI
To calculate the PKI, a polynomial function, Formula (1) is used.
4 2 2
n k m
PKI=⋅αβXX+⋅ ⋅X (1)
nk m
∑∑i ∑ i j
n=1 i m=1 k=1 ij⋅
where
PKI is the Propane Knock Index of the gaseous fuel;
X is the (normalized) mole fraction of component i or component j in the gaseous fuel;
α is a coefficient relating to component i in the gaseous fuel; α values are given in Table A.1
(α values not listed in Table A.1 shall be assumed zero(0));
β is a coefficient relating to combinations of components i and j in the gaseous fuel;
β values are given in Table A.1 (β values not listed in Table A.1 shall be assumed zero(0));
i is an index indicating a gaseous fuel component from the range CH , C H , C H , n-C H ,
4 2 6 3 8 4 10
i-C H , n-C H , i-C H , neo-C H , CO , CO, H or N ;
4 10 5 12 5 12 5 12 2 2 2
j is an index indicating a gaseous fuel component from the range C H , C H , n-C H , i-C H ,
2 6 3 8 4 10 4 10
k n-C H , i-C H , neo-C H , CO , CO, H or N ;
5 12 5 12 5 12 2 2 2
m 1, 2
n 1, 2
1 to 4
The result of Formula (1) is only valid if all of the following conditions are met:
a. the composition of the gaseous fuel used as input for Formula (1) complies with the limits/ranges listed
in Table 2;
b. the total mole percentage of the gaseous fuel used as input for Formula (1) is 100 %, or unity in the case
of using mole fractions;
c. the PKI value resulting from Formula (1) is ≤ 20.
+
To account for the presence of hexanes and higher hydrocarbons (denoted as hexanes ) and hydrogen sulfide
in the gaseous fuel under investigation scaling factors are used. These factors convert the effect of said
components on the knock resistance of the gas to that of methane and n-pentane respectively. The method
to adjust the methane and n-pentane mole fractions used as input for Formula (1) is given in Formulae (2)
and (3).
XX    ,=−03⋅X (2)
′
CH 44CH C 6+
XX=+XX+⋅13, (3)
nC51Hn25′ CH12 HS26C +
oSIST prEN ISO 17507-2:2024
ISO/DIS 17507-2:2024(en)
where
X is the adjusted mole fraction of methane in the gaseous fuel;
CH4’
X is the initial (normalized) mole fraction of methane in the gaseous fuel;
CH4
+
X + is the (normalized) mole fraction of hexanes in the gaseous fuel;
C6
X is the adjusted mole fraction of n-pentane in the gaseous fuel;
nC5H12’
X is the initial (normalized) mole fraction of n-pentane in the gaseous fuel;
nC5H12
X is the (normalized) mole fraction of hydrogen sulfide in the gaseous fuel.
H2S
Step 2: Calculation of the MN
PKI
To calculate the MN , a polynomial function, Formula (4) is used:
PKI
2 3 4 5 6
MN = a · PKI + a · PKI + a · PKI + a · PKI + a · PKI + a · PKI + b (4)
PKI 1 2 3 4 5 6
where
MN is the PKI methane number of the gaseous fuel;
PKI
PKI is the Propane Knock Index of the gaseous fuel as calculated with Formula (1);
a a ,…, a is a coefficient; values are given in Table A.2;
1, 2 6
b is a coefficient; value is given in Table A.2.
The result of Formula (4) is only valid if all of the following conditions are met:
a. the PKI value used as input for Formula (4) is ≤ 20;
b. the MN value resulting from Formula (4)is ≥ 53.
PKI
5.4 Expression of results
For expression of the final result, the calculated methane number is expressed as an integer and the
method used should be noted. E.g., 74 MN per ISO 17507-2. Rounding to an integer value according to
PKI
[20]
ISO 80000-1 is recommended as a higher numerical resolution of the MN value is not relevant in
PKI
practice.
5.5 Uncertainty error and bias
The MN is calculated from the mole fraction composition of the gaseous fuel under review as sole input,
PKI
using two polynomial functions. The coefficients used in both polynomial functions have a fixed value,
meaning that for a given gaseous fuel composition there can only be one MN value. For the purpose of this
PKI
standard, the MN values thus calculated are deemed to be exact according to the PKI method. Hence, any
PKI
error or bias in an MN value arises solely from errors in the gaseous fuel compositions used as input.
PKI
The resulting uncertainty shall be estimated according to Annex D.
6 Example calculations
6.1 Example calculation 1
The determination of the MN (and PKI) of a gaseous fuel is illustrated here by an example calculation for a
PKI
gas with mole fractions expressed as percentages of 90 % methane and 10 % ethane.

oSIST prEN ISO 17507-2:2024
ISO/DIS 17507-2:2024(en)
This gaseous fuel meets the gas composition limits/ranges of the PKI method as given in Table 1 and its
composition adds up to 100 %, meaning that the PKI method can be applied.
For the example gas composition noted, Formula (1) for the calculation of the PKI of this gaseous fuel is
simplified to
PKI = XCH4 · αCH4 + (XCH4)2 · α(CH4)2 + (XCH4)3 · α(CH4)3 + (XCH4)4 · α(CH4)4 + XC2H6 · αC2H6 +
(XC2H6)2 · α(C2H6)2 +
(XC2H6)3 · α(C2H6)3 + (XC2H6)4 · α(C2H6)4 + XCH4 · XC2H6 · βCH4xC2H6
Based on the gaseous fuel composition, the methane mole fraction X and ethane mole fraction X
CH4 C2H6
amount to 0,9 and 0,1 respectively. Using these fractions and the relevant α- and β coefficients from Table A.1,
the calculation of the PKI of this gaseous fuel amounts to
PKI = 0,9 · 569,285 536 016 002 0 + (0,9)2 · −650,854 339 490 7 + (0,9)3 · 64,359 575 257 386 2 +
(0,9)4 · 17,214 959 222 053 6 + 0,1 · −645,099 966 662 855 0 + (0,1)2 · 694,229 376 857 102 0 +
(0,1)3 · −675,381 075 231 165 0 + (0,1)4 · 1 474,790 791 373 33 + 0,1 · 0,9 · 201,788 909 592 169
resulting in a PKI value of 3,443 after rounding to three decimals.
This PKI value meets the criterion of PKI ≤ 20 and thus can be used as input to Formula (4) for the calculation
of the MN of this gaseous fuel according to
PKI
2 3 4 5 6
MN = a · PKI + a · PKI + a · PKI + a · PKI + a · PKI + a · PKI + b
PKI 1 2 3 4 5 6
Using the PKI value of 3,443 and the a and b coefficients from Table A.2, the calculation of the MN of this
PKI
gaseous fuel amounts to
MNPKI = -9,757 977 · 3,443 + 1,484 961 · 3,4432 - 0,139 533 · 3,4433 + 0,007 031 306 · 3,4434 -
0,000 177 002 9 · 3,4435 + 0,000 001 751 212 · 3,4436 + 100
resulting in a MN value of 79 after rounding to an integer value.
PKI
This MN value meets the criterion of MN ≥ 53 and thus is a valid result of the PKI method for this
PKI PKI
example gaseous fuel.
6.2 Example calculation 2
The determination of the MN (and PKI) of a gaseous fuel is illustrated here by an example calculation for
PKI
a gas with mole fractions expressed as percentages of 84,5 % methane, 6,0 % ethane, 4,0 % propane, 1,5 %
+
i-butane, 0,5 % n-pentane, 0,4 % hexanes , 3,0 % nitrogen and 0,1 % hydrogen-sulfide.
This gaseous fuel meets the gas composition limits/ranges of the PKI method as given in Table 1 and its
composition adds up to 100 %, meaning that the PKI method can be applied.
Before calculating the PKI of this gaseous fuel, the knock resistance of the hexanes and higher hydrocarbons
+
(denoted as hexanes ) and hydrogen sulfide fractions in the gas needs to be accounted for. This is done by
adjusting the methane and n-pentane mole fractions of the gaseous fuel using Formulae (2) and (3)
XX    =−03,.⋅=X 84 50−⋅,,30 48= 43, 8 %
′
CH44CH C6+
XX =+ XX+⋅13, =+05,,,01+⋅1304,,= 112 %
nC51Hn25′ CH12 HS26C +
resulting in an adjusted gas composition comprising of 84,38 % methane, 6,0 % ethane, 4,0 % propane,
1,5 % i-butane, 1,12 % n-pentane and 3,0 % nitrogen.
For the adjusted gas composition noted, Formula (1) for the calculation of the PKI of this gaseous fuel is
simplified to
PKI = XCH4 · αCH4 + (XCH4)2 · α(CH4)2 + (XCH4)3 · α(CH4)3 + (XCH4)4 · α(CH4)4 + XC2H6 · αC2H6 +
(XC2H6)2 · α(C2H6)2 +
oSIST prEN ISO 17507-2:2024
ISO/DIS 17507-2:2024(en)
(XC2H6)3 · α(C2H6)3 + (XC2H6)4 · α(C2H6)4 + XCH4 · XC2H6 · βCH4 · C2H6 + XC3H8 · αC3H8 +
(XC3H8)2 · α(C3H8)2 +
(XC3H8)3 · α(C3H8)3 + (XC3H8)4 · α(C3H8)4 + XCH4 · XC3H8 · βCH4 · C3H8 + Xiso-C4H10 · αiso-
C4H10 +
(Xiso-C4H10)2 · α(iso-C4H10)2 + (Xiso-C4H10)3 · α(iso-C4H10)3 + (Xiso-C4H10)4 · α(iso-C4H10)4 +
XCH4 · Xiso-C4H10 · βCH4 · iso-C4H10 + (XCH4 · Xiso-C4H10)2 · β(CH4 · iso-C4H10)2 + XC2H6 · Xiso-
C4H10 · βC2H6 · iso-C4H10 +
Xn-C5H12 · αn-C5H12 + (Xn-C5H12)2 · α(n-C5H12)2 + (Xn-C5H12)3 · α(n-C5H12)3 + (Xn-C5H12)4 ·
α(n-C5H12)4 +
XCH4 · Xn-C5H12 · βCH4 · n-C5H12 + XC2H6 · Xn-C5H12 · βC2H6 · n-C5H12 + XC3H8 · Xn-C5H12 ·
βC3H8 · n-C5H12 +
XC3H8 · (Xn-C5H12)2 · βC3H8 · (n-C5H12)2 + (XC3H8)2 · Xn-C5H12 · β(C3H8)2 · n-C5H12 +
Xiso-C4H10- · Xn-C5H12 · βiso-C4H10 · n-C5H12 + XN2 · αN2 + (XN2)2 · α(N2)2 + (XN2)3 · α(N2)3 +
(XN2)4 · α(N2)4 +
XCH4 · XN2 · βCH4 · N2 + XC2H6 · XN2 · βC2H6 · N2 + XC2H6 · (XN2)2 · βC2H6 · (N2)2 + (XC2H6)2 ·
XN2 · β(C2H6)2 · N2 +
XC3H8 · XN2 · β
...