Puneet Varma (Editor)

Useful conversions and formulas for air dispersion modeling

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Various governmental agencies involved with environmental protection and with occupational safety and health have promulgated regulations limiting the allowable concentrations of gaseous pollutants in the ambient air or in emissions to the ambient air. Such regulations involve a number of different expressions of concentration. Some express the concentrations as ppmv and some express the concentrations as mg/m³, while others require adjusting or correcting the concentrations to reference conditions of moisture content, oxygen content or carbon dioxide content. This article presents a set of useful conversions and formulas for air dispersion modeling of atmospheric pollutants and for complying with the various regulations as to how to express the concentrations obtained by such modeling.

Contents

Converting air pollutant concentrations

The conversion equations depend on the temperature at which the conversion is wanted (usually about 20 to 25 degrees Celsius). At an ambient air pressure of 1 atmosphere (101.325 kPa), the general equation is:

p p m v = m g / m 3 ⋅ ( 0.08205 ⋅ T ) M

and for the reverse conversion:

m g / m 3 = p p m v ⋅ M ( 0.08205 ⋅ T )

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 atmospheric pressure in atmospheres
  • mol = gram mole

    • Correcting concentrations for altitude

    Atmospheric pollutant concentrations expressed as mass per unit volume of atmospheric air (e.g., mg/m³, µg/m³, 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

    As an example, given a concentration of 260 mg/m³ at sea level, calculate the equivalent concentration at an altitude of 1,800 meters:

    Ca = 260 × 0.9877 18 = 208 mg/m³ at 1,800 meters altitude

    Standard conditions for gas volumes

    A normal cubic meter (Nm³ ) 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 Nm³ 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 kmol of any ideal gas equals 22.414 Nm³ of that gas at 0 °C and 1 atmosphere of absolute pressure ... and 1 lbmol of any ideal gas equals 379.482 scf of that gas at 60 °F and 1 atmosphere of absolute pressure.

    Notes:

  • kmol = kilomole or kilogram mole
  • lbmol = pound mole

    • Windspeed conversion factors

    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/s = 2.237 statute mile/h = 1.944 knots
    1 knot = 1.151 statute mile/h = 0.514 m/s
    1 statute mile/h = 0.869 knots = 0.447 m/s

    Note:

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

    • References

    Useful conversions and formulas for air dispersion modeling Wikipedia
    (Text) CC BY-SA