# SIST EN ISO 20765-5:2022

(Main)## Natural gas - Calculation of thermodynamic properties - Part 5: Calculation of viscosity, Joule-Thomson coefficient, and isentropic exponent (ISO 20765-5:2022)

## Natural gas - Calculation of thermodynamic properties - Part 5: Calculation of viscosity, Joule-Thomson coefficient, and isentropic exponent (ISO 20765-5:2022)

This document specifies methods to calculate (dynamic) viscosity, Joule-Thomson coefficient, isentropic

exponent, and speed of sound, excluding density, for use in the metering of natural gas flow.

## Erdgas - Berechnung der thermodynamischen Eigenschaften - Teil 5: Berechnung der Viskosität, Joule-Thomson-Koeffizient und Isentropenexponent (ISO 20765-5:2022)

Dieses Dokument legt Verfahren zur Berechnung der (dynamischen) Viskosität, des Joule-Thomson-Koeffizienten, des Isentropenexponenten und der Schallgeschwindigkeit, mit Ausnahme der Dichte, zur Anwendung bei der Messung des Durchflusses von Erdgas fest.

## Gaz naturel - Calcul des propriétés thermodynamiques - Partie 5: Calcul de la viscosité, du coefficient de Joule-Thomson et de l'exposant isentropique (ISO 20765-5:2022)

Le présent document spécifie une méthode de calcul de la viscosité et d'autres propriétés, à l'exception de la densité, pour le mesurage du débit de gaz naturel.

## Zemeljski plin - Izračun termodinamičnih lastnosti - 5. del: Izračun viskoznosti, Joule-Thomsonovega koeficienta in isentropnega eksponenta (ISO 20765-5:2022)

Ta dokument določa metode za izračun (dinamične) viskoznosti, Joule-Thomsonovega koeficienta, isentropnega eksponenta in hitrosti zvoka, razen gostote, za uporabo pri merjenju pretoka zemeljskega plina.

### General Information

### Standards Content (Sample)

SLOVENSKI STANDARD

SIST EN ISO 20765-5:2022

01-september-2022

Zemeljski plin - Izračun termodinamičnih lastnosti - 5. del: Izračun viskoznosti,

Joule-Thomsonovega koeficienta in isentropnega eksponenta (ISO 20765-5:2022)

Natural gas - Calculation of thermodynamic properties - Part 5: Calculation of viscosity,

Joule-Thomson coefficient, and isentropic exponent (ISO 20765-5:2022)

Erdgas - Berechnung der thermodynamischen Eigenschaften - Teil 5: Berechnung der

Viskosität, Joule-Thomson-Koeffizient und Isentropenexponent (ISO 20765-5:2022)

Gaz naturel - Calcul des propriétés thermodynamiques - Partie 5: Calcul de la viscosité,

du coefficient de Joule-Thomson et de l'exposant isentropique (ISO 20765-5:2022)

Ta slovenski standard je istoveten z: EN ISO 20765-5:2022

ICS:

75.060 Zemeljski plin Natural gas

SIST EN ISO 20765-5:2022 en,fr,de

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

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SIST EN ISO 20765-5:2022

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SIST EN ISO 20765-5:2022

EN ISO 20765-5

EUROPEAN STANDARD

NORME EUROPÉENNE

May 2022

EUROPÄISCHE NORM

ICS 75.060

English Version

Natural gas - Calculation of thermodynamic properties -

Part 5: Calculation of viscosity, Joule-Thomson coefficient,

and isentropic exponent (ISO 20765-5:2022)

Gaz naturel - Calcul des propriétés thermodynamiques Erdgas - Berechnung der thermodynamischen

- Partie 5: Calcul de la viscosité, du coefficient de Joule- Eigenschaften - Teil 5: Berechnung der Viskosität,

Thomson et de l'exposant isentropique (ISO 20765- Joule-Thomson-Koeffizient und Isentropenexponent

5:2022) (ISO 20765-5:2022)

This European Standard was approved by CEN on 3 April 2022.

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-CENELEC 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-CENELEC Management

Centre has the same status as the official versions.

CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,

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

Poland, Portugal, Republic of North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and

United Kingdom.

EUROPEAN COMMITTEE FOR STANDARDIZATION

COMITÉ EUROPÉEN DE NORMALISATION

EUROPÄISCHES KOMITEE FÜR NORMUNG

CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels

© 2022 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 20765-5:2022 E

worldwide for CEN national Members.

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SIST EN ISO 20765-5:2022

EN ISO 20765-5:2022 (E)

Contents Page

European foreword . 3

2

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SIST EN ISO 20765-5:2022

EN ISO 20765-5:2022 (E)

European foreword

This document (EN ISO 20765-5:2022) has been prepared by Technical Committee ISO/TC 193

"Natural gas" in collaboration with Technical Committee CEN/TC 238 “Test gases, test pressures,

appliance categories and gas appliance types” the secretariat of which is held by AFNOR.

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 2022, and conflicting national standards

shall be withdrawn at the latest by November 2022.

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

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

Any feedback and questions on this document should be directed to the users’ national standards

body/national committee. A complete listing of these bodies can be found on the CEN website.

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,

Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland,

Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Republic of

North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the

United Kingdom.

Endorsement notice

The text of ISO 20765-5:2022 has been approved by CEN as EN ISO 20765-5:2022 without any

modification.

3

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SIST EN ISO 20765-5:2022

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SIST EN ISO 20765-5:2022

INTERNATIONAL ISO

STANDARD 20765-5

First edition

2022-04

Natural gas — Calculation of

thermodynamic properties —

Part 5:

Calculation of viscosity, Joule-

Thomson coefficient, and isentropic

exponent

Gaz naturel — Calcul des propriétés thermodynamiques —

Partie 5: Calcul de la viscosité, du coefficient de Joule-Thomson et de

l'exposant isentropique

Reference number

ISO 20765-5:2022(E)

© ISO 2022

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SIST EN ISO 20765-5:2022

ISO 20765-5:2022(E)

COPYRIGHT PROTECTED DOCUMENT

© ISO 2022

All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may

be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on

the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below

or ISO’s member body in the country of the requester.

ISO copyright office

CP 401 • Ch. de Blandonnet 8

CH-1214 Vernier, Geneva

Phone: +41 22 749 01 11

Email: copyright@iso.org

Website: www.iso.org

Published in Switzerland

ii

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SIST EN ISO 20765-5:2022

ISO 20765-5:2022(E)

Contents Page

Foreword .iv

Introduction .v

1 Scope . 1

2 Normative references . 1

3 Terms and definitions . 1

4 Background . 1

5 Viscosity, η . . 3

5.1 Viscosity as a function of temperature, pressure, and composition . 3

5.2 Viscosity as a function of temperature and mass density . 6

6 Other properties . 6

6.1 Preamble . 6

6.2 Joule-Thomson coefficient, μ . 8

6.3 Isentropic exponent, κ . 9

6.4 Speed of sound, W . 10

7 Example calculations .10

8 Conclusions .11

9 Reporting of results .11

Annex A (informative) Symbols and units .12

Annex B (informative) Example LBC viscosity function .13

Annex C (informative) Example routine to convert CV, RD, and CO mole fraction to an

2

equivalent C -C -N -CO mixture .15

1 3 2 2

Annex D (informative) Viscosity of methane .16

Bibliography .17

iii

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SIST EN ISO 20765-5:2022

ISO 20765-5:2022(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.

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).

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. Details of

any patent rights identified during the development of the document will be in the Introduction and/or

on the ISO list of patent declarations received (see www.iso.org/patents).

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, Subcommittee SC 1,

Analysis of natural gas, in collaboration with the European Committee for Standardization (CEN)

Technical Committee CEN/TC 238, Test gases, test pressures and categories of appliances, in accordance

with the agreement on technical cooperation between ISO and CEN (Vienna Agreement).

A list of all parts in the ISO 20765 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

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SIST EN ISO 20765-5:2022

ISO 20765-5:2022(E)

Introduction

This document gives simplified methods for the calculation of (dynamic) viscosity, Joule-Thomson

coefficient, and isentropic exponent for use in natural gas calculations in the temperature range −20 °C

to 40 °C, with absolute pressures up to 10 MPa, and only within the gas phase. For the Joule-Thomson

coefficient and isentropic exponent, the uncertainty of the formulae provided is greater than that

[1]

obtained from a complete equation of state such as GERG-2008 (see ISO 20765-2) but is considered to

be fit for purpose. The formulae given here are very simple.

v

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SIST EN ISO 20765-5:2022

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SIST EN ISO 20765-5:2022

INTERNATIONAL STANDARD ISO 20765-5:2022(E)

Natural gas — Calculation of thermodynamic properties —

Part 5:

Calculation of viscosity, Joule-Thomson coefficient, and

isentropic exponent

1 Scope

This document specifies methods to calculate (dynamic) viscosity, Joule-Thomson coefficient, isentropic

exponent, and speed of sound, excluding density, for use in the metering of natural gas flow.

2 Normative references

There are no normative references in this document.

3 Terms and definitions

No terms and definitions are listed in this document.

4 Background

The main motivation for this document is to provide simplified methods for the calculations required,

according to ISO 5167, to measure flow of high-pressure natural gas with an orifice plate meter.

Useful references for the work herein are given below:

a) ISO 5167-1:1991, Measurement of fluid flow in closed conduits — Part 1: Pressure differential devices

b) EN 5167-1:1997, Measurement of fluid flow by means of pressure differential devices — Part 1: Orifice

plates, nozzles and Venturi tubes inserted in circular cross-section conduits running full

c) ISO 5167-1:2003, Measurement of fluid flow by means of pressure differential devices inserted in

circular cross-section conduits running full — Part 1: General principles and requirements

d) ISO 5167-2:2003, Measurement of fluid flow by means of pressure differential devices inserted in

circular cross-section conduits running full — Part 2: Orifice plates

The basic mass flowrate, q, formula is:

C π

2

q= ε dP2⋅⋅Δ D (1)

4 4

1−β

where

C is a function of β, Re, and the type of orifice pressure tappings;

ε is a function of β, P, ΔP, and κ.

The symbols are defined in Annex A. The standards above differ in the functions for C and ε. Although

q is given by Formula (1), iteration is required since C is a function of Re, and Re is a function of q.

Similarly, given q in Formula (1) does not directly give ΔP since ε is a function of ΔP.

1

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SIST EN ISO 20765-5:2022

ISO 20765-5:2022(E)

The use of the formulae in ISO 5167 for calculating flowrate (q) for an orifice plate meter, over a typical

input range of temperature, pressure, differential pressure, and gas composition, gives the following

formula for the standard uncertainty, u, (when the only source of uncertainties is considered to be in

the calculation of the required gas thermophysical properties):

22

2 =±05,, 0 000 2 ⋅u ρρ/

()

molar or mass density

()

uq /q

()

22

+00,,000 60±⋅ 000 2 u ηη/ viscosity

() ()

(2)

22

isentropic exponent

()

+±0,,002 0 001 2 ⋅u κκ/

()

JJoule-Thomson coefficient

()

2 22

+− 0,,000 40±⋅ 000 2 u μμ/

()

Formula (2) may be used to estimate the required uncertainty for the calculation of the properties that

are part of this document.

For the mass flowrate expanded uncertainty (U) (coverage factor k=2, with a 95 % confidence interval)

to be less than 0,1 % it is required that

U ρρ/,< 01 %

()

U ηη/%< 85

()

(3)

U κκ/%< 25

()

U μμ/%< 125

()

For the uncertainty contribution of these properties to the complete flowrate uncertainty to be less

than 0,02 % requires that

U ρρ/,< 002 %

()

U ηη/%< 17

()

(4)

U κκ/%< 5

()

U μμ/ < 255 %

()

Thus, density needs to be calculated as accurately as possible, while the uncertainty in the calculation

of the other properties can be much higher, with a target uncertainty of less than about 25 % for a 0,1 %

[1]

uncertainty in the flowrate (k = 2). The use of the GERG-2008 equation of state provides calculations

of density that are generally within the required 0,1 % uncertainty.

2

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SIST EN ISO 20765-5:2022

ISO 20765-5:2022(E)

5 Viscosity, η

5.1 Viscosity as a function of temperature, pressure, and composition

There are many methods for the calculation of gas phase (dynamic) viscosity, some of which that

are based on theory are quite complicated (see Reference [10] for details). The Lohrenz-Bray-Clark

method (LBC) is relatively simple, requires minimal component data, and is a method that is widely

implemented, and is the method recommended here. One disadvantage is the sensitivity to the input

density; but for the application considered here, accurate densities will be available.

This method requires that the gas composition is available. With inputs of temperature, pressure, and

composition, the GERG-2008 equation of state (ISO 20765-2) may be used to obtain the molar density

required in the formulae below. When the composition is not known, the method in 5.2 may be used.

The formulae needed to implement this method are outlined below (Annex B contains an example

Visual Basic program), where the required parameters consist of the following component values for

the N components:

— molar mass M [g/mol]

i

— critical temperature T [K]

c,i

— critical pressure P [MPa]

c,i

3

— critical density ρ [mol/dm ]

c,i

— mole fraction x [mol/mol]

i

These mixture parameters may be estimated with the following formulae:

N

Mx= M (5)

mix ∑ ii

i=1

N

Tx= T (6)

c,mixc∑ ii,

i=1

N

Px= P (7)

c,mixc∑ ii,

i=1

N

x

i

V = (8)

c,mix ∑

ρ

c,i

i=1

The component values are obtained from any suitable source, e.g. ISO 20765-2:2015, Annex B.

3

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SIST EN ISO 20765-5:2022

ISO 20765-5:2022(E)

The viscosity of a natural gas mixture is calculated as:

4

η =+ηξ⋅−δ 1 (9)

()

mix

The generalized mixture viscosity, which is based on the pure fluid viscosities, is:

N

xMη

∑ ii i

i=1

η = (10)

mix

N

xM

ii

∑

i=1

The parameter ξ is dependent only on the molar mass and the critical temperature and pressure, and is

given as:

1 1 2

−

6 3

2 T P

M

c,mixc,mix

mix

ξ =u (11)

η

u u u

MT P

This formula is made dimensionless with the use of the following constants:

u = 0,·000 1 mPas

η

u = 1 g/ mol

M

(12)

u = 1 K

T

u = 0,101 325 MPa

P

The parameter δ in Formula (9) is density dependent, and given as:

23 4

δρ=+1,,023 0 23364 ++0,,58533ρρ−0 40758 0,093324ρ (13)

rr rr

ρρ=⋅V (14)

r c,mix

where ρ is the molar density at T and P, calculated from ISO 20765-2.

The pure fluid component viscosity is:

1 2

1

−

6 3

2 T P

M

ci,,ci

i

η =u α (15)

i η

u u u

M T P

where α is given as:

09, 4

TT≤=15,: α 34, ⋅ (16)

rr

0,625

TT>=15,: α 1,,778⋅⋅()4581− ,67 (17)

rr

The reduced temperature in these formulae is:

TT= /T (18)

ric,

From the experimental data given in References [3] to [9] the estimated uncertainty of this method is

about 4 % (95 % confidence interval). (Bias=-0,31 %, RMS=1,59 %). Note that using Formula (9) these

are predicted calculations. The experimental data was not used in the development of the method.

The number of points and ranges are:

4

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SIST EN ISO 20765-5:2022

ISO 20765-5:2022(E)

Total number of points 721

Temperature range 260 K to 344 K (−13 °C to 71 °C)

Pressure range 0,1 MPa to 12,7 MPa

Figure 1 shows the distribution of the errors compared with the following experimental data:

[3]

1) Carr (1953) 3 mixtures 55 points

[4]

2) Golubev (1959) 1 mixture 17 points

[5]

3) Gonzalez et al. (1970) 8 mixtures 35 points

[6]

4) Nabizadeh & Mayinger (1999) 1 mixture 32 points

[7]

5) Assael et al. (2001) 1 mixture 22 points

[8]

6) Schley et al. (2004) 3 mixtures 521 points

[9]

7) Langelandsvik et al. (2007) 2 mixtures 39 points

a) Y as a function of T b) Y as a function of P

Key

T temperature (K) Y viscosity error (%)

P pressure (MPa)

Figure 1 — Comparisons of viscosities calculated from the Lohrenz-Bray-Clark method

(Formula 9) with experimental data

If only bulk properties are available rather than a detailed composition, e.g. calorific value (CV), relative

density (RD), and CO mole fraction (x(CO )), then an equivalent N /CO /CH /C H mixture may be used

2 2 2 2 4 3 8

in Formula (9) for viscosity. This equivalent four component mixture has two unknown mole fractions

(for N and C H ), where the CO mole fraction is given and the CH mole fraction = 1-x(N )-x(CO )-

2 3 8 2 4 2 2

x(C H ). These two unknowns are determined from the provided input, e.g. CV and RD. The procedure

3 8

assumes an initial compression factor, Z (e.g. 0,997 5) and solves the linearized CV and RD equations.

An iterative routine updates Z until the method has converged, which is rapid since Z does not change

much with natural gas composition.

An example of implementation to calculate the equivalent mixture is given in Annex C. For an example

of viscosity of methane, see Annex D.

5

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SIST EN ISO 20765-5:2022

ISO 20765-5:2022(E)

5.2 Viscosity as a function of temperature and mass density

When only temperature and mass density are known (i.e. the gas composition is not known), the

following simple formula may be used:

2

η =+0,,01036 0 000033⋅+tD0,,000021⋅+0 00000017⋅D (19)

where

t is given in °C

3

D is given in kg/m

η is given in mPa·s

The estimated uncertainty of this method is about 5 % (95 % confidence interval) (Bias = 0,08 %, RMS

= 2,57 %). Note that Formula 19 was fitted to the experimental data, so the true uncertainty is actually

likely to be greater than 5 %. Figure 2 shows the distribution of the errors for the 721 data points.

a) Y as a function of T b) Y as a function of P

Key

T temperature (K) Y viscosity equation error (%)

P pressure (MPa)

Figure 2 — Comparisons of viscosity calculated from Formula 19 with experimental data

6 Other properties

6.1 Preamble

Other properties, including those listed in this section, are accurately calculated with the GERG-2008

[1]

equation of state (as detailed in ISO 20765-2). There are no existing widely used simple methods for

these properties (unlike the case above for viscosity), so new formulae were derived. To determine the

optimal formulae, a range of simulated natural gases (5 000 compositions) was generated based on the

limits, given in Table 1.

6

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SIST EN ISO 20765-5:2022

ISO 20765-5:2022(E)

Table 1 — Component or property limits

Mole fraction

Component or property

%

Lower limit Upper limit

N 0,05 7

2

CO 0,01 4

2

CH 80 98

4

C H 0,25 9

2 6

C H 0,01 3,5

3 8

n-C H 0,001 1

4 10

n-C H 0,001 0,2

5 12

n-C H 0,001 0,2

6 14

i-C H /n-C H 0,45 0,83

4 10 4 10

i-C H /n-C H 0,83 1,33

5 12 5 12

neo-C H /n-C H 0,01 0,015

5 12 5 12

C /C 0,2 0,4

n n-1

3

Gross CV (MJ/m ) 35 45

Composition values were generated uniformly for N , CO , and C H within this range; C H values

2 2 2 6 3 8

were obtained from the ratio limits (C /C ) with the C H value, and likewise for n-C H , n-C H ,

n n-1 2 6 4 10 5 12

and n-C H (with ratio limits of C H , n-C H , or n-C H , respectively). Composition values were then

6 14 3 8 4 10 5 12

obtained for i-C H , i-C H , and neo-C H from the ratio limits. The CH composition is the remainder,

4 10 5 12 5 12 4

and the mixture was rejected if the CH and CV values (as well as those for C H , n-C H , n-C H , and

4 3 8 4 10 5 12

n-C H values) were not within their ranges.

6 14

[1]

The GERG-2008 equation of state was then used to calculate the properties for all the mixtures in a

grid of temperatures and pressures over the range of interest. From these calculations it was observed

that the compositional variation was less than the temperature and pressure variation, and was within

the target uncertainty outlined in the introduction. Therefore, formulae only as a function of T and P

were sought (the compositional variation is accounted for in the final overall uncertainty.)

To determine the optimal formula, a bank of terms with powers of T and P (including fractional powers,

and positive and negative values) was used with a selection and fitting routine in an Excel Add-In. The

final formulae that achieved the desired requirements are very straightforward.

The recommended formulae are given in the following sections, along with a table of values (from the

formula), a table of bias errors, and a table of RMS errors (as absolute values and as percent). The RMS

may be interpreted as a standard uncertainty (coverage factor k=1).

The bias and RMS (root-mean-squared) errors with respect to the calculation of ISO 20765-2 (GERG-

[1]

2008 equation of state ) are (for any property Y):

K

1

formula gerg

Bias=−YY (20)

()k

∑

k

K

k=1

2

K K foormula gerg

2 Y −Y

1 1

k

formula gerg k

RMS=−YY RMS%= 100 (21)

()

k

∑∑k

gerg

K K

Y

k==1 k 1

k

where K is the number of test points (in this case 5 000).

The major contribution to the RMS comes from the compositional variation rather than from the

simplicity of the formula.

7

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SIST EN ISO 20765-5:2022

ISO 20765-5:2022(E)

6.2 Joule-Thomson coefficient, μ

Definition:

∂T

μ = (22)

∂P

H

Formula:

2

μ =⋅() 5,,94−0 042 tt+−()0,,01770+⋅00021 ⋅P (23)

where

°

t is given in C

P is absolute pressure given in MPa

μ is given in K/MPa

The data were fitted in the range 0 °C to 30 °C with absolute pressures to 10 MPa, but as shown in the

table below, the extrapolation outside of this range is acceptable.

Table 2 — Joule-Thomson coefficient values and bias errors

Joule-Thomson coefficient value

P P Bias

μ

MPa MPa K/MPa

K/MPa

10 4,59 4,38 4,17 3,96 3,75 3,54 3,33 10 0,43 0,19 0,08 0,04 0,03 0,03 0,02

8 5,38 5,09 4,81 4,52 4,24 3,95 3,66 8 0,06 0,04 0,05 0,07 0,07 0,06 0,03

6 5,99 5,65 5,30 4,96 4,61 4,27 3,93 6 -0,18 −0,05 0,03 0,08 0,09 0,07 0,02

4 6,43 6,04 5,66 5,27 4,88 4,50 4,11 4 -0,20 −0,04 0,06 0,10 0,10 0,06 −0,01

2 6,69 6,28 5,87 5,46 5,05 4,63 4,22 2 -0,12 0,01 0,09 0,11 0,09 0,03 −0,05

T (°C) -20 −10 0 10 20 30 40 T (°C) -20 −10 0 10 20 30 40

Table 3 — Joule-Thomson coefficient RMS and RMS% errors

P RMS P

RMS %

MPa K/MPa MPa

10 0,44 0,21 0,18 0,19 0,19 0,19 0,19 10 10,6 5,2 4,5 5,0 5,4 5,6 5,8

8 0,24 0,28 0,28 0,28 0,27 0,25 0,23 8 4,7 5,6 6,1 6,5 6,7 6,6 6,4

6 0,47 0,40 0,37 0,34 0,31 0,28 0,25 6 7,2 7,0 7,1 7,2 7,2 7,0 6,5

4 0,54 0,45 0,40 0,37 0,34 0,30 0,26 4 7,8 7,3 7,3 7,4 7,3 6,9 6,4

2 0,51 0,44 0,40 0,37 0,33 0,29 0,27 2 7,2 7,0 7,1 7,2 6,9 6,4 6,1

T (°C) -20 −10 0 10 20 30 40 T (°C) -20 −10 0 10 20 30 40

8

© ISO 2022 – All rights reserved

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SIST EN ISO 20765-5:2022

ISO 20765-5:2022(E)

6.3 Isentropic exponent, κ

Definition:

V ∂P

κ =− (24)

P ∂V

S

Formula:

2

κ =−()1,,30280 00057940⋅+tt()−+,,008437 0 00026580⋅⋅P+( ,003267−−⋅0,)00005517 tP⋅

(25)

where

t is given in °C

P is absolute pressure given in MPa

κ is dimensionless

The data were fitted in the range 0 °C to 20 °C with absolute pressures to 7,5 MPa, but as

**...**

SLOVENSKI STANDARD

oSIST prEN ISO 20765-5:2020

01-julij-2020

Zemeljski plin - Izračun termodinamičnih lastnosti - 5. del: Izračun Joule-

Thomsonovega koeficienta, isentropskega eksponenta in viskoznosti (ISO/DIS

20765-5:2020)

Natural gas - Calculation of thermodynamic properties - Part 5: Calculation of viscosity,

Joule-Thomson coefficient, and isentropic exponent (ISO/DIS 20765-5:2020)

Erdgas - Berechnung der thermodynamischen Eigenschaften - Teil 5: Berechnung der

Viskosität, Joule-Thomson-Koeffizient und Isentropenexponent (ISO/DIS 20765-5:2020)

Gaz naturel - Calcul des propriétés thermodynamiques - Partie 5: Calcul de la viscosité,

du coefficient de Joule-Thomson et de l'exposant isentropique (ISO/DIS 20765-5:2020)

Ta slovenski standard je istoveten z: prEN ISO 20765-5

ICS:

75.060 Zemeljski plin Natural gas

oSIST prEN ISO 20765-5:2020 en,fr,de

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

---------------------- Page: 1 ----------------------

oSIST prEN ISO 20765-5:2020

---------------------- Page: 2 ----------------------

oSIST prEN ISO 20765-5:2020

DRAFT INTERNATIONAL STANDARD

ISO/DIS 20765-5

ISO/TC 193/SC 1 Secretariat: NEN

Voting begins on: Voting terminates on:

2020-05-14 2020-08-06

Natural gas — Calculation of thermodynamic properties —

Part 5:

Calculation of viscosity, Joule-Thomson coefficient, and

isentropic exponent

Gaz naturel — Calcul des propriétés thermodynamiques —

Partie 5: Calcul de la viscosité, du coefficient de Joule-Thomson et de l'exposant isentropique

ICS: 75.060

THIS DOCUMENT IS A DRAFT CIRCULATED

This document is circulated as received from the committee secretariat.

FOR COMMENT AND APPROVAL. IT IS

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TO SUBMIT, WITH THEIR COMMENTS,

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©

PROVIDE SUPPORTING DOCUMENTATION. ISO 2020

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oSIST prEN ISO 20765-5:2020

ISO/DIS 20765-5:2020(E)

COPYRIGHT PROTECTED DOCUMENT

© ISO 2020

All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may

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ii © ISO 2020 – All rights reserved

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oSIST prEN ISO 20765-5:2020

ISO/DIS 20765-5:2020(E)

Contents Page

Foreword .iv

Introduction .v

1 Scope . 1

2 Normative references . 1

3 Terms and definitions . 1

4 Background . 1

5 Viscosity (η) . 3

5.1 Viscosity as a function of temperature, pressure, and composition . 3

5.2 Viscosity as a function of temperature and mass density . 6

6 Other Properties . 6

6.1 Preamble . 6

6.2 Joule-Thomson coefficient (μ) . 8

6.3 Isentropic exponent (κ) . 8

6.4 Speed of Sound (W) . 9

7 Example calculations .10

8 Conclusions .10

9 Reporting of results .10

Annex A (Normative) Symbols and Units .11

Annex B (Informative) Example LBC Viscosity Function .12

Annex C (Informative) Example Routine to Convert CV, RD, and CO mole fraction to an

2

Equivalent C -C -N -CO Mixture .14

1 3 2 2

Annex D (Informative) Viscosity of methane .15

Bibliography .16

© ISO 2020 – All rights reserved iii

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oSIST prEN ISO 20765-5:2020

ISO/DIS 20765-5:2020(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.

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).

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. Details of

any patent rights identified during the development of the document will be in the Introduction and/or

on the ISO list of patent declarations received (see www .iso .org/ patents).

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, Subcommittee SC 1,

Analysis of Natural gas.

A list of all parts in the ISO 20765 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 © ISO 2020 – All rights reserved

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oSIST prEN ISO 20765-5:2020

ISO/DIS 20765-5:2020(E)

Introduction

This document gives simplified methods for the calculation of (dynamic) viscosity, Joule-Thomson

coefficient, and isentropic exponent for use in natural gas calculations in the temperature range −20 °C

to 40 °C, with absolute pressures up to 10 MPa, in the gas phase. For the Joule-Thomson coefficient and

isentropic exponent, the uncertainty of the equations provided is greater than that obtained from a

[2]

complete equation of state such as the GERG-2008 equation (1) (ISO 20765-2 ) but is considered to be

fit for purpose. The equations given here are very simple.

© ISO 2020 – All rights reserved v

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oSIST prEN ISO 20765-5:2020

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oSIST prEN ISO 20765-5:2020

DRAFT INTERNATIONAL STANDARD ISO/DIS 20765-5:2020(E)

Natural gas — Calculation of thermodynamic properties —

Part 5:

Calculation of viscosity, Joule-Thomson coefficient, and

isentropic exponent

1 Scope

This part of ISO 20765 specifies a method to calculate viscosity and other properties, excluding density,

for use in the metering of natural gas flow.

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 7504, Gas analysis — Vocabulary

ISO 14532, Natural gas — Vocabulary

ISO 20765-1, Natural gas — Calculation of thermodynamic properties — Part 1: Gas phase properties for

transmission and distribution applications

ISO 20765-2, Natural gas — Calculation of thermodynamic properties — Part 2: Single-phase properties

(gas, liquid, and dense fluid) for extended ranges of application

ISO 80000-5:2007, Quantities and units — Part 5: Thermodynamics

3 Terms and definitions

No terms and definitions are listed in this document.

4 Background

The main motivation for this standard is to provide simplified methods for the calculations required,

according to ISO 5167, to measure flow of high-pressure natural gas with an orifice plate meter.

Useful references for the work herein are given below:

a) ISO 5167-1:1991, Measurement of fluid flow in closed conduits – Part 1. Pressure differential devices –

Section 1.1: Specification for square-edged orifice plates, nozzles and Venturi tubes inserted in circular

cross-section conduits running full, (BS 1042:Section 1.1:1992).

b) ISO 5167-1:1997, Measurement of fluid flow by means of pressure differential devices – Part 1:

Orifice plates, nozzles and Venturi tubes inserted in circular cross-section conduits running full”,

(BS 1042-1.1:1992 renumbered, incorporating Amendment No.1 (renumbering the BS as BS EN

ISO 5167-1:1997), and Amendment No.1 to BS EN ISO 5167-1:1997)

c) ISO 5167-1:2003, Measurement of fluid flow by means of pressure differential devices inserted in

circular cross-section conduits running full – Part 1: General principles and requirements

© ISO 2020 – All rights reserved 1

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oSIST prEN ISO 20765-5:2020

ISO/DIS 20765-5:2020(E)

d) ISO 5167-2:2003, Measurement of fluid flow by means of pressure differential devices inserted in

circular cross-section conduits running full – Part 2: Orifice plates

The basic mass flowrate equation is

C π

2

q= ε dP2⋅⋅Δ ρ (1)

4

4

1−β

where

C is a function of β, Re, and the type of orifice pressure tappings;

ε is a function of β, P, ΔP, and κ.

The symbols are defined in Annex A. The standards above differ in the functions for C and ε. Although

q is given by equation (1), iteration is required since C is a function of Re, and Re is a function of q.

Similarly, given q in equation (1) does not directly give ΔP since ε is a function of ΔP.

The use of the equations in ISO-5167 (2003) for calculating flowrate (q) for an orifice plate meter,

over a typical input range of temperature, pressure, differential pressure, and gas composition, gives

the following uncertainty equation (when the only source of uncertainties is considered to be in the

calculation of the required gas thermophysical properties):

2 2 2

[u(q)/q] = [ 0.5 ± 0.0002 ] ⋅[u(ρ)/ρ] (molar or mass density)

2 2

+ [ 0.0006 ± 0.0002 ] ⋅[u(η)/η] (viscosity)

2 2

+ [ 0.002 ± 0.0012 ] ⋅[u(κ)/κ] (isentropic exponent)

2 2

+ [ −0.0004 ± 0.0002 ] ⋅[u(μ)/μ] (Joule-Thomson coefficient) (2)

This equation can be used to estimate the required uncertainty for the calculation of the properties

that are part of this standard.

For the mass flowrate expanded uncertainty (U) (coverage factor k=2, with a 95 % confidence interval)

to be less than 0.1 % it is required that

U(ρ)/ρ < 0.1 %

U(η)/η < 85 %

U(κ)/κ < 25 %

U(μ)/μ < 125 % (3)

For the uncertainty contribution to be less than 0.02 % requires that

U(ρ)/ρ < 0.02 %

U(η)/η < 17 %

U(κ)/κ < 5 %

U(μ)/μ < 25 % (4)

Thus, density needs to be calculated as accurately as possible, while the uncertainty in the calculation

of the other properties can be much higher, with a target uncertainty no better than about 25 % for a 0.1

% uncertainty in the flowrate (k=2). The use of the GERG-2008 equation of state provides calculations

of density that are generally within the required 0.1 % uncertainty.

2 © ISO 2020 – All rights reserved

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oSIST prEN ISO 20765-5:2020

ISO/DIS 20765-5:2020(E)

5 Viscosity (η)

5.1 Viscosity as a function of temperature, pressure, and composition

There are many methods for the calculation of gas phase (dynamic) viscosity, some of which that are

based on theory are quite complicated (see reference 11 for details). The Lohrenz-Bray-Clark method is

relatively simple, requires minimal component data, and is a method that is widely implemented, and

is the method recommended here. One disadvantage is the sensitivity to the input density; but for the

[3]

application considered here, accurate densities will be available. The original reference is given in .

This method requires that the gas composition is available. With inputs of temperature, pressure,

[1,2]

and composition, the GERG-2008 equation of state (ISO 20765-2) can be used to obtain the molar

density required in the equations below. When the composition is not known, the methods in Section

3.2 can be used.

The equations needed to implement this method are outlined below (Annex B contains an example

Visual Basic program), where the required parameters consist of the following pure fluid values:

molar mass M [g/mol]

i

critical temperature T [K]

c,i

critical pressure P [MPa]

c,i

3

critical density ρ [mol/dm ]

c,i

These mixture parameters can be estimated with the following equations:

N

Mx= M (5)

∑

mix ii

i=1

N

Tx= T (6)

c,mixc∑ ii,

i=1

N

Px= P (7)

∑

c,mixcii,

i=1

N

x

i

V = (8)

c,mix ∑

ρ

c,i

i=1

The pure fluid values can be obtained from any suitable source, e.g., ISO 20765-2 (Annex B).

The viscosity of a natural gas mixture can be calculated as

4

η = η + ξ ( δ – 1 ) (9)

mix

The generalized mixture viscosity, which is based on the pure fluid viscosities, is

N

xMη

∑

ii i

i=1

η = (10)

mix

N

xM

∑ ii

i=1

where

x is the component mole fraction.

i

© ISO 2020 – All rights reserved 3

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oSIST prEN ISO 20765-5:2020

ISO/DIS 20765-5:2020(E)

The parameter ξ is dependent only on the molar mass and the critical temperature and pressure, and is

given as

1 2

1

−

6 3

2 T P

M

c,mixc,mix

mix

ξ =u (11)

η

u u u

MT P

This equation is made dimensionless with the use of the following constants:

u = 0.0001 mPa·s

η

u = 1 g/mol

M

u = 1 K

T

u = 0.101325 MPa (12)

P

The parameter δ in equation 9 is density dependent, and given as

2 3 4

δ = 1.023 + 0.23364 ρ + 0.58533 ρ - 0.40758 ρ + 0.093324 ρ (13)

r r r r

ρ = V ×ρ (14)

r c,mix

where

ρ is the molar density at T and P, calculated from ISO 20765-2.

lThe pure fluid component viscosity is

1 1 2

−

2 T 6 P 3

M

ci,,ci

i

η =u α (15)

i η

u u u

M T P

where

α is obtained with

0.94

T ≤ 1.5: α = 3.4 ×T (16)

r r

0.625

T > 1.5: α = 1.778 ×( 4.58 ×T − 1.67 ) (17)

r r

The reduced temperature in these equations is

T = T / T (18)

r c,i

[4-10]

From the experimental data given in references, the estimated uncertainty of this method is about

4 % (95 % confidence interval). (Bias=-0.31 %, RMS=1.59%). Note that using equation 9 these are

predicted calculations. The experimental data was not used in the development of the equation.

The number of points and ranges are

Total number of points 721

Temperature range 260 to 344 K (−13 to 71 °C)

Pressure range 0.1 to 12.7 MPa

Figures 1 and 2 show the distribution of the errors compared with the following experimental data:

4 © ISO 2020 – All rights reserved

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oSIST prEN ISO 20765-5:2020

ISO/DIS 20765-5:2020(E)

1) N.L.Carr, Viscosities of natural gas components and mixtures, Institute of Gas Technology Research

Bulletin 23, (1953)

3 mixtures, 55 points

2) I.F. Golubev, Viscosity of Gases and Gas Mixtures: A Handbook, p.214 (1959)

1 mixture, 17 points

3) M. Gonzalez, B.E. Eakin and A.L. Lee, Monograph on API Research Project 65, American Petroleum

Institute (1970)

8 mixtures, 35 points

4) H. Nabizadeh and F. Mayinger, High Temperatures-High Pressures, 31:601-612 (1999)

1 mixture, 32 points

5) M.J. Assael, N.K. Dalaouti and V. Vesovic, Int. J. Thermophysics, 22:61-71 (2001)

1 mixture, 22 points

6) P. Schley, M. Jaeschke, C. Kuchenmeister and E. Vogel, Int. J. Thermophysics, 25:1623-1651 (2004)

3 mixtures, 521 points

7) L.I.Langelandsvik, S.Solvang, M.Rousselet, I.N.Metaxa and M.J.Assael, Int. J. Thermophysics,

28:1120–1130 (2007)

2 mixtures, 39 points

Figure 1 — & Figure 2 — Comparisons of viscosities calculated from the Lohrenz-Bray-Clark

method (equation 9) with experimental data as a function of temperature (Figure 1) and

pressure (Figure 2)

If only bulk properties are available rather than a detailed composition, e.g., calorific value (CV),

relative density (RD), and CO mole fraction (x(CO )), then an equivalent N /CO /CH /C H mixture can

2 2 2 2 4 3 8

be used in equation 9 for viscosity. This equivalent four component mixture has two unknown mole

fractions (for N and C H ), where CO mole fraction is given and CH mole fraction=1-x(N )-x(CO )-

2 3 8 2 4 2 2

x(C H ). These two unknowns are determined from the CV and RD. The procedure assumes an initial

3 8

Z (e.g., 0.9975) and solves the linearized CV and RD equations. An iterative routine updates Z until the

method has converged, which is rapid since Z does not change

**...**

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