Gas Flow Conversions. Equations and Calculator Mass flow, flow at standard (base, normal) conditions, and flow at actual (flowing) 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.

Calculation

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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), s=second, psi=pound per square inch, psia=psi (absolute), psig=psi (gage), scfd=std cfd, scfh=std cfh, scfm=std cfm, std=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 and calculators can be found at Univ. Florida (2006), Process (2003), and Istos (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.

Istos. 2003. Gas compressibility factor (calculator uses Redlich Kwong equation). http://jacq.istos.com.au/tech/zrk.html.

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

University of Florida. 2006 (retrieved). Real gases: Deviation from ideal behavior. http://www.chem.ufl.edu/~itl/2045/lectures/lec_e.html.

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