Useful conversions and formulas for air dispersion modeling

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. [ [http://www.air-dispersion.com/formulas.html Air Dispersion Modeling Conversions and Formulas] ]

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:

:$mathrm\{ppmv\}\; =\; mathrm\{mg\}/mathrm\{m\}^3cdot\; frac\{(0.08205cdot\; T)\}\{M\}$

and for the reverse conversion:

:$mathrm\{mg\}/mathrm\{m\}^3\; =\; mathrm\{ppmv\}cdot\; frac\{M\}\{(0.08205cdot\; T)\}$

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

The following equation can be used to correct a measured pollutant concentration in an emitted gas (containing a measured O₂ content) to an equivalent pollutant concentration in an emitted gas containing a specified reference amount of O₂: [40 U.S. Code of Federal Regulations, Chapter I, Part 60, Appendix B, Performance Specification 2.]

:$C\_r\; =\; C\_mcdotfrac\{(20.9-r)\}\{(20.9-m)\}$

Thus, a measured NOx concentration of 45 ppmv (dry basis) in a gas having 5 volume % O₂ is
45 × ( 20.9 - 3 ) ÷ ( 20.9 - 5 ) = 50.7 ppmv (dry basis) of NOx when corrected to a gas having a specified reference O₂ content of 3 volume %.

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: [40 U.S. Code of Federal Regulations, Chapter I, Part 60.]

:$C\_r\; =\; C\_mcdotfrac\; \{r\}\{m\}$

Thus, a measured particulates concentration of 0.1 grain per dscf in a gas that has 8 volume % CO₂ is
0.1 × ( 12 ÷ 8 ) = 0.15 grain per dscf when corrected to a gas having a specified reference CO₂ 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 10¹² and the USA billion which is 10⁹.

ee also

* Standard conditions of temperature and pressure
* Units conversion by factor-label
* Atmospheric dispersion modeling
* Roadway air dispersion modeling
* Bibliography of atmospheric dispersion modeling
* Accidental release source terms
* Choked flow

References

External links

* More conversions and formulas useful in air dispersion modeling are available in the feature articles at [http://www.air-dispersion.com www.air-dispersion.com] .
* [http://www.epa.gov/eogapti1/toc/full_toc.htm U.S. EPA tutorial course] has very useful information.