Air pollutant concentrations, as measured or as calculated by air pollution dispersion modeling,[1] must often be converted or corrected to be expressed as required by the regulations issued by various governmental agencies. Regulations that define and limit the concentration of pollutants in the ambient air or in gaseous emissions to the ambient air are issued by various national and state (or provincial) environmental protection and occupational health and safety agencies.

Such regulations involve a number of different expressions of concentration. Some express the concentrations as ppmv (parts per million by volume) and some express the concentrations as mg/m3 (milligrams per cubic meter), while others require adjusting or correcting the concentrations to reference conditions of moisture content, oxygen content or carbon dioxide content. This article presents methods for converting concentrations from ppmv to mg/m3 (and vice versa) and for correcting the concentrations to the required reference conditions.

All of the concentrations and concentration corrections in this article apply only to air and other gases. They are not applicable for liquids.

Converting air pollutant concentrations

The conversion equations depend on the temperature at which the conversion is wanted (usually about 20 to 25 °C). At an ambient sea level atmospheric pressure of 1 atm (101.325 kPa):

APC-Conc.png

Notes:
  • 1 atm = absolute pressure of 101.325 kPa
  • mol = gram mole and kmol = 1000 gram moles
  • 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.
  • Although ppmv and mg/m3 have been used for the examples in all of the following sections, concentrations such as ppbv (i.e., parts per billion by volume), volume percent, mole percent and many others may also be used for gaseous pollutants.
  • Particulate matter (PM) in the atmospheric air or in any other gas cannot be expressed in terms of ppmv, ppbv, volume percent or mole percent. PM is most usually (but not always) expressed as mg/m3 of air or other gas at a specified temperature and pressure.
  • For gases, volume percent = mole percent
  • 1 volume percent = 10,000 ppmv (i.e., parts per million by volume) with a million being defined as 106.
  • Care must be taken with the concentrations expressed as ppbv to differentiate between the British billion which is 1012 and the USA billion which is 109 (also referred to as the long scale and short scale billion, respectively).

Correcting concentrations for altitude

Air 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. The concentration decrease is directly proportional to the pressure decrease with increasing altitude. Some governmental regulatory jurisdictions require industrial sources of air pollution to comply with sea level standards corrected for altitude. In other words, industrial air pollution sources located at altitudes well above sea level must comply with significantly more stringent air quality standards than sources located at sea level (since it is more difficult to comply with lower standards). For example, New Mexico's Department of the Environment has a regulation with such a requirement.[2] [3]

The derivation of an equation for relating atmospheric pressure to altitude has been published online by the Portland State Aerospace Society[4] and that equation can be rearranged and used as follows:

APC-Altit.png

As an example, given an air pollutant concentration of 260 mg/m3 at sea level, the equivalent pollutant concentration at an altitude of 2800 meters (2.8 km) is:
  • C h = 260 × [ { 288 - (6.5)(2.8) } / 288 ] 5.2558
  • = 260 × 0.71 = 185 mg/m3

Note:
  • The above equation for the decrease of air pollution concentrations with increasing altitude is applicable only for about the first 10 km of altitude in the troposphere (the lowest atmospheric layer) and is estimated to have a maximum error of about 3 percent. However, 10 km of altitude is sufficient for most purposes involving air pollutant concentrations.

Correcting concentrations for reference conditions

Many environmental protection agencies have issued regulations that limit the concentration of pollutants in air pollution emissions and define the reference conditions applicable to those concentration limits. For example, such a regulation might limit the concentration of nitrogen oxides (NOx) to 55 ppmv in a dry combustion flue gas (at a specified reference temperature and pressure) corrected to 3 volume percent of oxygen (O2) in the dry gas. As another example, a regulation might limit the concentration of total particulate matter to 200 mg/m3 of an emitted gas (at a specified reference temperature and pressure) corrected to a dry basis and further corrected to 12 volume percent carbon dioxide (CO2) in the dry gas.

Environmental agencies in the USA often use the terms "dscf" or "scfd" to denote a "standard" cubic foot of dry gas. Likewise, they often use the terms "dscm" or "scmd" to denote a "standard" cubic meter of gas. Since there is no universally accepted set of "standard" temperature and pressure, such usage can be and is very confusing. It is strongly recommended that the reference temperature and pressure always be clearly specified when stating gas volumes or gas flow rates.[5]

Correcting to a dry basis

If a gaseous emission sample is analyzed and found to contain water vapor and a pollutant concentration of say 40 ppmv, then 40 ppmv 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:

APC-Dry.png

As an example, a wet basis concentration of 40 ppmv in a gas having 10 volume percent water vapor would have an equivalent dry basis concentration of:

  • C dry basis = 40 ÷ ( 1 - 0.10 )
  • = 44.4 ppmv

Correcting to a reference oxygen content

The following equation can be used to correct a measured pollutant concentration in a dry emitted gas with a measured O2 content to an equivalent pollutant concentration in a dry emitted gas with a specified reference amount of O2:[6]

APC-O2.png

As an example, when corrected to a dry gas having a specified reference O2 content of 3 volume %, a measured NOx concentration of 45 ppmv in a dry gas that has a measured 5 volume % O2 is:

  • C r = 45 × ( 20.9 - 3 ) ÷ ( 20.9 - 5 )
  • = 50.7 ppmv of NOx

Note:
  • The measured gas concentration C m must first be corrected to a dry basis before using the above equation.

Correcting to a reference carbon dioxide content

The following equation can be used to correct a measured pollutant concentration in an emitted gas (containing a measured CO2 content) to an equivalent pollutant concentration in an emitted gas containing a specified reference amount of CO2:[7]

APC-CO2.png

As an example, when corrected to a dry gas having a specified reference CO2 content of 12 volume %, a measured particulates concentration of 200 mg/m3 in a dry gas that has a measured 8 volume % CO2 is:

  • C r = 200 × ( 12 ÷ 8 )
  • = 300 mg/m3

Note:
  • The measured gas concentration C m must first be corrected to a dry basis before using the above equation.

References

  1. ^ M.R. Beychok (2005), Fundamentals of Stack Gas Dispersion, 4th Edition, ISBN 0-9644588-0-2.
  2. ^ Draft Programmatic Environmental Impact Statement (EIS) for Stockpile Stewardship and Management, Volume 4 See section 03.08 by going to pdf pages 135-136 for discussion of New Mexico's regulation.
  3. ^ Air Quality Impact Analysis, Section 2.2 Developed for the United States Bureau of Land Management, Socorro Field Office, New Mexico. See pdf page 18 of 44 pdf pages.
  4. ^ A Quick Derivation relating altitude to air pressure December 2004.
  5. ^ Reference conditions of gas temperature and pressure
  6. ^ David A. Lewandowski (1999), Design of Thermal Oxidation Systems for Volatile Organic Compounds, 1st Edition, CRC Press, ISBN 1-56670-410-3.
  7. ^ Same as Reference 6