RUHR-UNIVERSITÄT BOCHUM

Training – Density Calculations of

Metrology for LNG | Aberdeen, Scotland | 26.10.2018

N. von Preetzmann, P. Eckmann, M. Richter

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LNG Research at RUB

P. Eckmann R. Kleinrahm N. v. Preetzmann

R. Span R. Lentner M. Richter

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Primary Densimeter for “Metrology for LNG”

Technical specifications

• T-range: (90 to 300) K• p-range: (0.05 to 12) MPa• Hom. Densities (liquid and gas)

& saturated liquid density• U(ρ(T,p,x)) = 0.02 % (k = 2)

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LNG Custody Transfer

General Formula for Calculating the LNG Energy Transferred(According to GIIGNL - LNG Custody Transfer Handbook)

E : the total net energy transferred from the loading facilities to the LNG carrier, or from the LNG carrier to the unloading facilities.

VLNG : the volume of LNG loaded or unloaded in m³.

ρLNG : the density of LNG loaded or unloaded in kg/m³.

GCVS,LNG: the gross calorific value of the LNG loaded or unloadedin MMBTU/kg.

Eg,displaced : the net energy of the displaced gas in MMBTU

E = VLNG ∙ ρLNG(T, p, x) ∙ GCVS,LNG − Eg, displaced [MMBTU]

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LNG Density Calculation Methods – cf. CTH by GIIGNL

Reference manual for custody transfer procedures and equipment

• Widely used in Europe and Asia

• Including recommended methods for LNG property determination

• No accurate in-situ densimeters at LNG operating conditions available(large uncertainties)

• Determination of density by means of calculation methods is recommended

• A variety of calculation methods exists {

In general:• Fundamental Equation of States• Cubic Equation of States• Simplified Engineering Models

International Group of Liquefied Natural Gas Importers (2017)

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LNG Density Calculation Methods – cf. CTH by GIIGNL

Revised Klosek-McKinley method (RKM) of R. D. McCarty (1980)

• ISO Standard (ISO 6578)

• Well-established for LNG custody transfer

• Calculation of saturated liquid densities

• Range of validity: T < 115 K

• Uncertainty: Δρ/ρ = 0.10 %

• Results often deviate from true density atpressures above saturation pressure

• Not usable for processes at elevated pressures (e.g., small scale applications)

𝑀𝑚𝑖𝑥

𝜌𝑚𝑖𝑥= 𝑣𝑚𝑖𝑥(𝑇) =

𝑖

𝑥𝑖 ∙ 𝑣𝑖 − 𝑘1 + 𝑘2 − 𝑘1 ∙𝑥𝑁2

0.0425∙ 𝑥𝐶𝐻4

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LNG Density Calculation Methods – cf. CTH by GIIGNL

Enhanced Revised Klosek-McKinley (ERKM) method for saturated and pressurized LNG

• Range of validity: 100 ≤ T / K ≤ 135 Kp ≤ 10 MPa

• Uncertainties: for 100 ≤ T / K ≤ 115, Δρ/ρ = 0.10 %

for 115 < T / K ≤ 135, Δρ/ρ = 0.15 %

𝜌𝐿𝑁𝐺 = 𝜌𝑅𝐾𝑀 ∙ 1 + 𝑘𝑝

𝑘𝑝 = (𝑝 − 𝑝𝑠,𝑚𝑖𝑥) ∙ 4.06 ∙𝑇𝑃𝐶

𝑇𝑃𝐶 − 𝑇

1.79

The original RKM Pressure-dependent term

Approximation for the mixture‘s vapor pressure

Pseudo-critical temperature to avoid deviations at higher temperatures

Tietz, Richter, Kleinrahm, Span, Fuel Proc. Technol. 165 (2017) 19-26

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LNG Density Calculation Methods – cf. CTH by GIIGNL

Tietz, Richter, Kleinrahm, Span, Fuel Proc. Technol. 165 (2017) 19-26

Performance of the ERKM