Turbine Meter

This application calculates the various values associated with the flow through a turbine meter, including flow rate, adjusted minimum flow rate, estimated pressure differential, rangeability, and the rated capacity adjustment factor. It supports multiple calculation methods and adjusts meter capacity for actual operating pressure, temperature, gas properties, and compressibility conditions.

Note: This calculator does not predict turbine rotor speed. Always consult the specific manufacturer’s documentation regarding meter speed limits to avoid premature meter failure.

Background

There are various methods and devices used to measure the flow of gas at a specific location. These devices are generally referred to as “meters.” One type is the inferential meter, which infers the volumetric flow rate from another parameter. In the case of a turbine meter, the volumetric flow rate is computed based on the velocity of a spinning turbine rotor.

Manufacturers generally rate a turbine meter at a specific inlet pressure. It has been a long-standing industry practice to use turbine meters under conditions different from the rated conditions. In many cases, a meter is used when the actual flow through it exceeds its rated capacity. This allows smaller meters to be used for larger applications.

Effect of Operating Pressure on Capacity

There is essentially one parameter that affects the “capacity” of a turbine-type meter, the operating pressure. Because gas is compressible, as the operating pressure changes, the gas density also changes. The density change affects both the gas velocity and the number of standard volumes that pass through the meter for a given flow velocity. If the pressure is increased, the gas density increases, and therefore more standard volumes are contained within the physical volume of gas passing through the meter, resulting in more total standard volumes passing through over a specific period of time.

Rangeability and Flow Limits

Manufacturers publish both a minimum and a maximum flow rate for turbine meters. Operating within these values ensures that gas flow measurements are within specified accuracy limits. The rangeability is an indication of the ratio between the maximum and minimum flow rates. The minimum and maximum capacity ratings, as well as the rangeability, are all affected by operating conditions. The differential pressure across the meter increases with increasing operating pressure and flow rate.

The maximum amount of gas that can be safely and accurately passed through a specific turbine meter depends on the speed at which the turbine rotor is spinning. Each meter has a specific speed limit; exceeding this limit will likely result in immediate or premature failure of the meter. If the turbine speed needs to be limited, a flow-limiting orifice or nozzle can be installed upstream of the meter.

Equations

Generic Turbine Meter Flow

As implemented in GASCalc, this method uses an equation derived from several industry references. The maximum capacity at flowing conditions is given by:

Q_F = Q_R \times \left[\frac{P_F}{P_R}\right] \times \left[\frac{SG_R}{SG}\right]^{0.5} \times \left[\frac{T_R}{T_F}\right]^{0.5} \times \left[\frac{Z_R}{Z_F}\right]^{0.5}

Q_F = Q_R \times \left[\frac{P_F}{P_R}\right] \times \left[\frac{SG_R}{SG}\right]^{0.5} \times \left[\frac{T_R}{T_F}\right]^{0.5} \times \left[\frac{Z_R}{Z_F}\right]^{0.5}

Where:
Q_F — Maximum Meter Capacity at Flowing (Metered) Conditions, ft³
Q_R — Maximum Meter Capacity at Rated Conditions Converted to Base Conditions, ft³
P_F — Pressure at Flowing (Metered) Conditions, psia
P_R — Pressure at Rated Conditions, psia
SG_R — Specific Gravity at Rated Conditions
SG — Specific Gravity of Flowing (Metered) Gas
T_R — Temperature at Rated Conditions, °R (assumed to be 60°F)
T_F — Temperature at Flowing (Metered) Conditions, °R
Z_R — Compressibility Factor at Rated Conditions
Z_F — Compressibility Factor at Flowing (Metered) Conditions
P_F = P_FG + P_ATM, where P_ATM is Atmospheric Pressure at the Metered Location (psia) and P_FG is Gauge Pressure at Flowing Conditions (psig)
P_R = P_RG + P_{R_ATM}, where P_{R_ATM} is Atmospheric Pressure at Rated Conditions (psia) and P_RG is Gauge Pressure at Rated Conditions (psig)

Where Q_R is first derived from:

Q_R = Q_{RATED} \times \left[\frac{P_{BR}}{P_B}\right] \times \left[\frac{T_B}{T_{BR}}\right] \times \left[\frac{Z_B}{Z_{BR}}\right]

Q_R = Q_{RATED} \times \left[\frac{P_{BR}}{P_B}\right] \times \left[\frac{T_B}{T_{BR}}\right] \times \left[\frac{Z_B}{Z_{BR}}\right]

Where:
Q_R — Meter Maximum Capacity at Rated Conditions Converted to Specified Base Pressure and Temperature, cf
Q_RATED — Meter Maximum Capacity at Rated Base Pressure and Temperature, ft³
P_BR — Base Pressure at Rated Conditions, psia
P_B — Base Pressure, psia
T_B — Base Temperature, °R
T_BR — Base Temperature at Rated Conditions, °R
Z_B — Compressibility Factor at Specified Base Conditions
Z_BR — Compressibility Factor at Rated Base Conditions [Assumed to be 1.0]

Turbine Meter Minimum Flow

The adjusted minimum flow rate at flowing conditions is calculated as:

Q_{FMIN} = Q_{RMIN} \times \left[\frac{P_F}{P_R}\right]^{0.5} \times \left[\frac{SG_R}{SG}\right]^{0.5} \times \left[\frac{T_R}{T_F}\right]^{0.5} \times \left[\frac{Z_R}{Z_F}\right]^{0.5}

Q_{FMIN} = Q_{RMIN} \times \left[\frac{P_F}{P_R}\right]^{0.5} \times \left[\frac{SG_R}{SG}\right]^{0.5} \times \left[\frac{T_R}{T_F}\right]^{0.5} \times \left[\frac{Z_R}{Z_F}\right]^{0.5}

Where:
Q_FMIN — Minimum Meter Capacity at Flowing (Metered) Conditions, ft³
Q_RMIN — Minimum Meter Capacity at Rated Conditions Converted to Base Conditions, ft³
P_F — Pressure at Flowing (Metered) Conditions, psia
P_R — Pressure at Rated Conditions, psia
SG_R — Specific Gravity at Rated Conditions
SG — Specific Gravity of Flowing (Metered) Gas
T_R — Temperature at Rated Conditions, °R [Assumed to be 60°F]
T_F — Temperature at Flowing (Metered) Conditions, °R
Z_R — Compressibility Factor at Rated Conditions
Z_F — Compressibility Factor at Flowing (Metered) Conditions

Where Q_RMIN is first derived from:

Q_{RMIN} = Q_{RATED\text{-}MIN} \times \left[\frac{P_{BR}}{P_B}\right] \times \left[\frac{T_B}{T_{BR}}\right] \times \left[\frac{Z_B}{Z_{BR}}\right]

Q_{RMIN} = Q_{RATED\text{-}MIN} \times \left[\frac{P_{BR}}{P_B}\right] \times \left[\frac{T_B}{T_{BR}}\right] \times \left[\frac{Z_B}{Z_{BR}}\right]

Where:
Q_RMIN — Meter Minimum Capacity at Rated Conditions Converted to Specified Base Pressure and Temperature, ft³
Q_RATED-MIN — Meter Minimum Capacity at Rated Base Pressure and Temperature, ft³
P_BR — Base Pressure at Rated Conditions, psia
P_B — Base Pressure, psia
T_B — Base Temperature, °R
T_BR — Base Temperature at Rated Conditions, °R
Z_B — Compressibility Factor at Specified Base Conditions
Z_BR — Compressibility Factor at Rated Base Conditions [Assumed to be 1.0]

Turbine Meter Rangeability

The rangeability represents the maximum-to-minimum capacity ratio of the meter at the specified operating conditions:

RANGE = \frac{Q_F}{Q_{FMIN}}

RANGE = \frac{Q_F}{Q_{FMIN}}

Where:
RANGE — Turbine Meter Rangeability
Q_F — Meter Maximum Capacity at Flowing (Metered) Conditions, ft³
Q_FMIN — Meter Minimum Capacity at Flowing (Metered) Conditions, ft³

Turbine Meter Pressure Differential

The estimated pressure differential across the meter at flowing conditions is:

DP_F = DP_R \times \left[\frac{P_F}{P_R}\right] \times \left[\frac{SG}{SG_R}\right] \times \left[\frac{T_R}{T_F}\right] \times \left[\frac{Z_R}{Z_F}\right] \times \left[\frac{Q_F}{Q_R}\right]^2 + DP_{FRICTION}

DP_F = DP_R \times \left[\frac{P_F}{P_R}\right] \times \left[\frac{SG}{SG_R}\right] \times \left[\frac{T_R}{T_F}\right] \times \left[\frac{Z_R}{Z_F}\right] \times \left[\frac{Q_F}{Q_R}\right]^2 + DP_{FRICTION}

Where:
DP_F — Pressure Differential at Flowing (Metered) Conditions, psia
DP_R — Pressure Differential at Rated Conditions, psia
P_F — Pressure at Flowing (Metered) Conditions, psia
P_R — Pressure at Rated Conditions, psia
SG — Specific Gravity of Flowing (Metered) Gas
SG_R — Specific Gravity at Rated Conditions
T_R — Temperature at Rated Conditions, °R [Assumed to be 60°F]
T_F — Temperature at Flowing (Metered) Conditions, °R
Z_R — Compressibility Factor at Rated Conditions
Z_F — Compressibility Factor at Flowing (Metered) Conditions
Q_F — Maximum Meter Capacity at Flowing (Metered) Conditions, ft³
Q_R — Maximum Meter Capacity at Rated Conditions Converted to Base Conditions, ft³
DP_FRICTION — Frictional Pressure Loss, psia

Rated Capacity Adjustment Factor

The rated capacity adjustment factor represents the multiplication factor required to convert the meter’s rated capacity to its actual capacity at the specified base and flowing conditions:

FACTOR = \frac{Q_F}{Q_{RATED}}

FACTOR = \frac{Q_F}{Q_{RATED}}

Where:
FACTOR — Rated Capacity Adjustment Factor, dimensionless
Q_F — Meter Maximum Capacity at Flowing (Metered) Conditions, cf
Q_RATED — Meter Maximum Capacity at Rated Base Pressure and Temperature, cf

Case Guide

Part 1: Create Case

Input Parameters

Part 2: Outputs/Reports

Results

References

• American Gas Association — Measurement, GEOP Series Book M-1, 1993.
• American Gas Association — Measurement of Natural Gas by Turbine Meters, Report No. 7, 2006.

FAQ