S-G-03–Specifications for the approval of type of gas meters, ancillary devices and associated measuring instruments

Category: Gas
Issue date:
Effective date:
Revision number: 1
Supersedes: LMB-EG-08 and S-G-03

Appendix C: Algorithms used to evaluate the performance of cone-shaped differential pressure meters

Unless the applicant of the cone-shaped differential pressure (CSDP) meter specifies otherwise, the meter's performance shall be evaluated using an equation for differential pressure measuring elements similar to those presented in AGA Report No.3: Orifice Metering of Natural Gas and Other Related Hydrocarbon Fluids – Concentric, Square-edged Orifice Meters, Part 3: Natural Gas Applications (American Petroleum Institute Manual of Petroleum Measurement Standards, chapter 14.3.3, fourth edition, 2013). The equation differs in order to account for the physical differences between the two types of meters. The equation for the mass flow rate for CSDP meters can be written as shown below. An important difference is that the discharge coefficient (Cd) is not determined by the modelling equation used in AGA Report No. 3, Part 3, but rather by using an empirical equation developed through experimentation specific to the meter type. It has been shown that Cd can be assumed as reasonably constant in the calibrated flow range. It will be corrected by using a Re correlated meter factor in the flow computer.

Eqn. (A.1)

Q = (Q m) ÷ rho

Eqn. (A.2)

(Q m i) = (pi ÷ 4) × (C d i) × (uppercase D^2) × beta^2 × (E v) × (F ext) × (Y1)


Eqn. (A.3)

(E v) = 1 ÷ (√(1-beta^4))

Eqn. (A.4)

(F ext) = √(2 × (rho f) × (Delta P))

The following empirical equation has been developed to describe the upstream gas expansion factor:

Eqn. (A.5)

(Y1) = 1 – (0.649 + (0.696 × beta^4)) × (Delta P) ÷ (K prime × P)

The beta ratio as described in AGA Report No. 3, Part 3 is not directly applicable. A similar ratio has been successfully developed for CSDP meters and is defined by the following relationship:

Eqn. (A.6)

beta = √(1 – ((lowercase d^2) ÷ (uppercase D^2)))

Use of data in flow computers

Knowing, from a reference standard, the true mass flow rate at each of the prescribed test points (Qref(i)), Cd,(i) can be calculated using the following equation:

Eqn. (A.7)

(Cd i) = (4 × (Q ref i)) ÷ (pi × (uppercase D^2) × beta^2 × (E v) × (F ext) × (Y1))

In the first method, once the values for Cd have been calculated, the values will be used to determine the relationship between Re and the meter factor (Mf(i)) at each test point. The Mf(i) values will then be programmed in the flow computer.

Eqn. (A.8)

(M f i) = (C d i) ÷ (C d, mean)

Eqn. (A.9)

R e = (rho × V × (uppercase D)) ÷ mu

List of symbols used in appendix C
Symbol Description
ß beta ratio
ΔP pressure differential across meter
Cd discharge coefficient
Cd,mean mean Cd (value programmed as a constant Cd in flow computer)
Cd(i) discharge coefficient at the specific Reynolds number (Re)
d outside diameter of the cone
D the inside diameter of the meter pipe
Ev approach velocity
Fext expansion factor
K' isentropic exponent
Mf,(i) meter factor at the specific Reynolds number (Re)
P static pressure absolute
Qm mass flow rate
Q non-converted volumetric flow rate (not converted to reference conditions of standard pressure and standard temperature)
Qref(i) mass flow rate through the reference standard at the specific Reynolds number (Re) or (i) test point, where i = 1, 2, 3, 4, …
Re Reynolds number
Y1 upstream gas expansion factor
V bulk velocity of flowing gas
ρ gas density at actual flowing gas conditions
µ dynamic viscosity of the flowing gas

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