oSIST prEN ISO 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)

A method to calculate viscosity and other properties, 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/DIS 20765-5:2020)

Dieser Teil von ISO 20765 legt ein Verfahren fest zur Berechnung der Viskosität und anderen Eigenschaften, jedoch nicht die Dichte, zur Anwendung bei der Messung von Erdgasströmen.

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)

Zemeljski plin - Izračun termodinamičnih lastnosti - 5. del: Izračun viskoznosti, Joule-Thomsonovega koeficienta in isentropnega eksponenta (ISO/DIS 20765-5:2020)

General Information

• Status: Not Published
• Public Enquiry End Date: 01-Aug-2020
• ICS: 75.060 - Natural gas
• Technical Committee: DPL - Gas supply
• Current Stage: 4020 - Public enquire (PE) (Adopted Project)
• Start Date: 20-May-2020
• Due Date: 07-Oct-2020
• Completion Date: 03-Aug-2020
• Ref Project: prEN ISO 20765-5 - Natural gas - Calculation of thermodynamic properties - Part 5: Calculation of viscosity, Joule-Thomson coefficient, and isentropic exponent (ISO/DIS 20765-5:2020)

Standards Content (sample)

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.

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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
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
THEREFORE SUBJECT TO CHANGE AND MAY
NOT BE REFERRED TO AS AN INTERNATIONAL
STANDARD UNTIL PUBLISHED AS SUCH.
IN ADDITION TO THEIR EVALUATION AS
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Reference number
NATIONAL REGULATIONS.
ISO/DIS 20765-5:2020(E)
RECIPIENTS OF THIS DRAFT ARE INVITED
TO SUBMIT, WITH THEIR COMMENTS,
NOTIFICATION OF ANY RELEVANT PATENT
RIGHTS OF WHICH THEY ARE AWARE AND TO
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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oSIST prEN ISO 20765-5:2020
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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

Equivalent C -C -N -CO Mixture ......................................................................................................................................................14

1 3 2 2

Annex D (Informative) Viscosity of methane ............................................................................................................................................15

Bibliography .............................................................................................................................................................................................................................16

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oSIST prEN ISO 20765-5:2020
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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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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.
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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

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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
q= ε dP2⋅⋅Δ ρ (1)
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.
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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]
critical temperature T [K]
c,i
critical pressure P [MPa]
c,i
critical density ρ [mol/dm ]
c,i
These mixture parameters can be estimated with the following equations:
Mx= M (5)
mix ii
i=1
Tx= T (6)
c,mixc∑ ii,
i=1
Px= P (7)
c,mixcii,
i=1
V = (8)
c,mix ∑
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
η = η + ξ ( δ – 1 ) (9)
mix

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

xMη
ii i
i=1
η = (10)
mix
∑ ii
i=1
where
x is the component mole fraction.
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The parameter ξ is dependent only on the molar mass and the critical temperature and pressure, and is

given as
1 2
6 3
2 T P
M    
 
c,mixc,mix
mix
ξ =u (11)
   
 
u u u
 
MT   P 
This equation is made dimensionless with the use of the following constants:
u = 0.0001 mPa·s
u = 1 g/mol
u = 1 K
u = 0.101325 MPa (12)
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
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:

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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
...