# Dispersion Modelling Conversions and Formulas

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# Converting air pollutant concentrationsEdit

The conversion equations depend on the temperature at which the conversion is wanted (usually about 20 to 25 degrees Centigrade). At an ambient air pressure of 1 atmosphere, the general equation is:

**ppmv = mg/m ^{3} × °K × 0.08205 ÷ MW**

and for the reverse conversion:

**mg/m ^{3} = ppmv × MW ÷ (0.08205 · °K)**

where: | |

ppmv
| = air pollutant concentration, in parts per million by volume |
---|---|

mg/m
^{3} | = milligrams of pollutant per cubic meter of air |

°K
| = atmospheric temperature in degrees Kelvin = 273.15 + °C |

0.08205
| = Universal Gas Law constant in (atm·liter)/(gmol·°K) |

MW
| = molecular weight of the air pollutant (dimensionless) |

Notes:

- Pollution regulations in the United States typically reference their pollutant limits to an ambient temperature of 20 to 25 °C as noted above. In most other nations, the reference ambient temperature for pollutant limits may be 0 °C or other values.
- 1 percent by volume = 10,000 ppmv (i.e., parts per million by volume).
- atm = absolute atmosperic pressure in atmospheres
- gmol = gram mole

# Correcting concentrations for altitudeEdit

Atmospheric pollutant concentrations expressed as mass per unit volume of atmospheric air (e.g., mg/m^{3}, ug/m^{3}, etc.) at sea level will decrease with increasing altitude because the atmospheric pressure decreases with increasing altitude.

The change of atmospheric pressure with altitude can be obtained from this equation:

**P _{a} = 0.9877^{ a}**

Given an atmospheric pollutant concentration at an atmospheric pressure of 1 atmosphere (i.e., at sea level altitude), the concentration at other altitudes can be obtained from this equation:

**C _{a} = C × 0.9877^{ a}**

where: | |

a
| = altitude, in 100's of meters |
---|---|

P
| = atmospheric pressure at altitude a, in atmospheres |

C
| = Concentration at sea level altitude, in mass per unit volume |

C
_{a} | = Concentration at altitude a, in mass per unit volume |

As an example, given a concentration of 260 mg/m^{3} at sea level, calculate the equivalent concentration at an altitude of 1,800 meters:

C_{a} = 260 × 0.9877^{ 18} = 208 mg/m^{3} at 1,800 meters altitude

# Standard conditions for gas volumesEdit

A normal cubic meter (Nm^{3}) is the metric expression of gas volume at standard conditions and it is usually (*but not always*) defined as being measured at 0 °C and 1 atmosphere of pressure.

A standard cubic foot (scf) is the USA expression of gas volume at standard conditions and it is often (*but not always*) defined as being measured at 60 °F and 1 atmosphere of pressure. There are other definitions of standard gas conditions used in the USA besides 60 °F and 1 atmosphere.

That being understood:

**1 Nm ^{3} of any gas (measured at 0 °C and 1 atmosphere of absolute pressure) equals 37.326 scf of that gas (measured at 60 °F and 1 atmosphere of absolute pressure).**

**1 kgmol of any ideal gas equals 22.414 Nm ^{3} of that gas ... and 1 lbmol of any ideal gas equals 379.482 scf of that gas.**

Notes:

- kgmol = kilogram mole
- lbmol = pound mole

# Windspeed conversion factorsEdit

Meteorological data includes windspeeds which may be expressed as statute miles per hour, knots, or meters per second. Here are the conversion factors for those various expressions of windspeed:

**1 m/sec = 2.237 statute mile/hr = 1.942 knots**

**1 knot = 1.152 statute mile/hr = 0.515 m/sec**

**1 statute mile/hr = 0.868 knots = 0.447 m/sec**

Note:

- 1 statute mile = 5,280 feet = 1,609 meters

# Correcting for reference conditionsEdit

Many environmental protection agencies have issued regulations that limit the concentration of pollutants in gaseous emissions and define the reference conditions applicable to those concentration limits. For example, such a regulation might limit the concentration of NOx to 55 ppmv in a dry combustion exhaust gas corrected to 3 volume percent O_{2}. As another example, a regulation might limit the concentration of particulate matter to 0.1 grain per standard cubic foot (i.e., scf) of dry exhaust gas corrected to 12 volume percent CO_{2}.

Environmental agencies in the USA often denote a standard cubic foot of dry gas as "dscf" or as "scfd". Likewise, a standard cubic meter of dry gas is often denoted as "dscm" or "scmd" (again, by environmental agencies in the USA).

*Correcting to a dry basis*Edit

If a gaseous emission sample is analyzed and found to contain water vapor and a pollutant concentration of X, then X should be designated as the "wet basis" pollutant concentration. The following equation can be used to correct the measured "wet basis" concentration to a "dry basis" concentration:

**(1) dry basis concentration = ( wet basis concentration ) ÷ ( 1 - w )**

where: | |

w | = fraction of the emitted exhaust gas, by volume, which is water vapor |
---|

Thus, a wet basis concentration of 40 ppmv in a gas having 10 volume percent water vapor would have a dry basis concentration = 40 ÷ ( 1 - 0.10 ) = 44.44 ppmv.

*Correcting to a reference oxygen content*Edit

The following equation can be used to correct a measured pollutant concentration in an emitted gas (containing a measured O_{2} content) to an equivalent pollutant concentration in an emitted gas containing a specified reference amount of O_{2}:

**(2) C _{r} = C_{m} × ( 20.9 - r ) ÷ ( 20.9 - m )**

where: | |

C_{r} | = corrected concentration in a dry gas having a specified reference volume % O _{2} of r |
---|---|

C_{m} | = measured concentration in a dry gas having a measured volume % O_{2}of m |

Thus, a measured NOx concentration of 45 ppmv (dry basis) in a gas having 5 volume % O_{2} =
45 × ( 20.9 - 3 ) ÷ ( 20.9 - 5 ) = 50.7 ppmv (dry basis) of NOx when corrected to a gas having a specified reference O_{2} content of 3 volume %.

*Correcting to a reference carbon dioxide content*Edit

The following equation can be used to correct a measured pollutant concentration in an emitted gas (containing a measured CO_{2} content) to an equivalent pollutant concentration in an emitted gas containing a specified reference amount of CO_{2}:

**(3) C _{r} = C_{m} × ( r ÷ m )**

where: | |

C_{r} | = corrected concentration in a dry gas having a specified reference volume % CO _{2} = r |
---|---|

C_{m} | = measured concentration in a dry gas having a measured volume % CO _{2} = m |

Thus, a measured particulates concentration of 0.1 grain per dscf in a gas that has 8 volume % CO_{2} =
0.1 × ( 12 ÷ 8 ) = 0.15 grain per dscf when corrected to a gas having a specified reference CO_{2} content of 12 volume %.

Notes:

- Although ppmv and grains per dscf have been used in the above examples, concentrations such as ppbv (i.e., parts per billion by volume), volume percent, grams per dscm and many others may also be used.
- 1 percent by volume = 10,000 ppmv (i.e., parts per million by volume).
- Care must be taken with the concentrations expressed as ppbv to differentiate between the British billion which is 10
^{12}and the USA billion which is 10^{9}. - Equation (1) above is from "40 CFR, Chapter I, Part 60, Appendix A-3, Test Method 4".
- Equation (2) above is from "40 CFR, Chapter I, Part 60, Appendix B, Performance Spec. 2".
- Equation (3) above is from "40 CFR, Chapter I, Part 60".
- CFR = United States Code of Federal Regulations

# External linksEdit

- More conversions and formulas useful in air dispersion modeling are available in the public domain feature articles at www.air-dispersion.com.
- U.S. EPA tutorial course has very useful information.

_______________

Milton Beychok

January 2006