Gas Flow Conversions. Equations and Calculator

Mass flow, flow at standard (base, normal) conditions, and flow at actual (flowing) conditions

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 © 2014 LMNO Engineering, Make selections: Enter Specific Gravity Enter Molecular Weight Research, and Software, Ltd. www.LMNOeng.com Enter Standard Flow Enter Actual Flow Enter Mass Flow Specific Gravity, S: Molecular Weight, M: gram/mole Compressibility Factor, Z: Standard Temperature, Ts: Fahrenheit, F Rankine, R Celsius, C Kelvin, K Standard Pressure (abs), Ps: atm psia inch H2O (60F) abs inch Mercury (60F) abs mbar absolute bar absolute N/m2 absolute kPa absolute mm Mercury (0C) abs Actual Temperature, Ta: Fahrenheit, F Rankine, R Celsius, C Kelvin, K Actual Pressure (abs), Pa: atm psia inch H2O (60F) abs inch Mercury (60F) abs mbar absolute bar absolute N/m2 absolute kPa absolute mm Mercury (0C) abs Standard Flow, Qs: std ft3/s, cfs std ft3/min, scfm std ft3/hr, scfh std ft3/day, scfd std Thousand cfh, Mcfh std Million cfd, MMcfd std m3/s std m3/min std m3/hr std m3/day Actual Flow, Qa: actual ft3/s, cfs actual ft3/min, acfm actual ft3/hr, acfh actual ft3/day, acfd actual Thousand cfh, Mcfh actual Million cfd, MMcfd actual m3/s actual m3/min actual m3/hr actual m3/day Mass Flow, W: slug/s lb/s lb/hr lb/day kg/s kg/hr kg/day Actual Density, ρa: lb/ft3 slug/ft3 kg/m3 g/cm3 Standard Density, ρs: lb/ft3

Units: abs=absolute, acfd=actual cfd, acfh=actual cfh, acfm=actual cfm, cfd=cubic foot per day, cfh=cubic foot per hour, cfm=cubic foot per minute, cfs=cubic foot per second, cm=centimeter, g=gram, hr=hour, kg=kilogram, km=kilometer, kPa=kiloPascal, lb=pound, m=meter, mbar=millibar, mm=millimeter, Mcfh=thousand cfh, MMcfd=million cfd, N/m2=Newton per square meter (same as Pascal), psi=pound per square inch, psia=psi (absolute), psig=psi (gage), s=second, scfd=std cfd, scfh=std cfh, scfm=std cfm, std=standard conditions.

Equations
In the gas flow discipline, flowrates are often expressed as "flow at standard conditions". Standard conditions are synonymous with the term "base conditions" or "normal conditions". The calculation on this page converts between mass flow (W), flow at standard conditions (Qs), and flow at actual (flowing) conditions (Qa). The equations use SI units, but our calculation allows a variety of units with all of the unit conversions handled internally by the program.

Standard (Base) Conditions
For the natural gas industry in North America and OPEC (Organization of Petroleum Exporting Countries), standard conditions are typically Ps=14.73 psia and Ts=60oF. IUPAC (International Union of Pure and Applied Chemistry) uses Ts=0oC and Ps=1 bar. Some gas flows related to environmental engineering are based on standard conditions of Ts=15oC or 20oC and Ps=101.325 kPa (1 atmosphere). Standard conditions vary from industry to industry and have varied over the years within the same field, so it is important to know the standard temperature and pressure that a stated "standard flow" is based upon. Wikipedia (2006) has a good discussion of standard conditions.

Notes about some confusions in the gas industry: In English units, the abbrevation "M" means thousand and "MM" means million. In metric units, "M" means mega which means million. You may see the notation "Nm3/s" which is a metric (SI) unit for "Normal m3/s". Normal is the same as standard or base, which can be confused with Newton (unit of force) since both have the same abbreviation. We don't use the unit "Nm3/s" on this page; instead, we call it "std m3/s".

Variables
The units refer to the units that must be used in the equations shown above. However, a variety of units may be used in our calculation.
M = Molecular weight of the actual (flowing) gas (kg/mol). For example, methane (CH4) has a molecular weight of 0.016042 kg/mol. Compute molecular weight using our calculator.
Mair = Molecular weight of standard air = 0.02896443 kg/mol (CRC, 1983).
Pa = Absolute pressure at actual (flowing) conditions (N/m2 absolute).
Ps = Absolute pressure at standard (base) conditions (N/m2 absolute).
Qa = Flowrate at actual (flowing) conditions (m3/s).
Qs = Flowrate at standard (base) conditions (m3/s).
Ru = Universal gas constant = 8.3144126 N-m/mol-K (CRC, 1983, p. F-192).
S = Specific gravity of flowing gas (note that Sair=1). For example CH4 has S=MCH4/Mair= 0.016042 / 0.2896443 = 0.554
Ta = Absolute temperature at actual (flowing) conditions (K).
Ts = Absolute temperature at standard (base) conditions (K).
W = Mass flowate (kg/s).
Z = Gas compressibility factor which represents the gas's deviation from ideal gas behavior. Typically 1.0 at standard conditions. Typically decreases as pressure increases then increases at high pressure. Can be as low as 0.4 or so and up to 2 or so. Exact computation depends on make-up of the gas, gas critical pressure and temperature, and actual temperature and pressure. Additional information can be found at Process (2003).
ρa = Greek letter rho. Density at actual (flowing) conditions, kg/m3.
ρs = Greek letter rho. Density at standard (base) conditions, kg/m3.

Error Messages given by calculation
The following are error messages shown if input values are improper:
"Need Z > 0", "Need Pa , Ps > 0", "Need Ta , Ts > 0.0 K", "Need S > 0", "Need M > 0", "Need Qa > 0", "Need Qs > 0", "Need W > 0".

References
Chemical Rubber Company (CRC). 1983. CRC Handbook of Chemistry and Physics. Weast, Robert C., editor. 63rd edition. CRC Press, Inc. Boca Raton, Florida. USA.

Process Associates of America. 2003. Gas compressibility factor (calculator uses Redlich Kwong equation). http://www.processassociates.com/process/property/z_factor.htm.

Wikipedia. 2006. Standard conditions for temperature and pressure. http://en.wikipedia.org/wiki/Standard_temperature_and_pressure.

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Molecular weight

Weymouth, Panhandle A, Panhandle B flowrate, pressure

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Darcy-Weisbach incompressible flow

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