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.
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 or 1.01325 bar), the general equation is:
and for the reverse conversion:
where: | |
mg/m3 | = milligrams of pollutant per cubic meter of air at sea level atmospheric pressure and T |
ppmv | = air pollutant concentration, in parts per million by volume |
T | = ambient temperature in K = 273. + °C |
0.082057338 | = Universal gas constant in L atm mol−1 K−1 |
M | = molecular mass (or molecular weight) of the air pollutant |
Notes:
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. [5] [6]
The change of atmospheric pressure with altitude (<20 km) can be obtained from this equation: [7]
Given an air pollutant concentration at sea-level atmospheric pressure, the concentration at higher altitudes can be obtained from this equation:
where: | |
h | = altitude, in km |
---|---|
P | = atmospheric pressure at sea level |
Ph | = atmospheric pressure at altitude h |
C | = Air pollutant concentration, in mass per unit volume at sea level atmospheric pressure and specified temperature T |
Ch | = Concentration, in mass per unit volume at altitude h and specified temperature T |
As an example, given an air pollutant concentration of 260 mg/m3 at sea level, calculate the equivalent pollutant concentration at an altitude of 2800 meters:
Note:
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 (at a specified reference temperature and pressure) corrected to 3 volume percent 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 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.
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:
where: | |
C | = Concentration of the air pollutant in the emitted gas |
---|---|
w | = fraction of the emitted exhaust gas, by volume, which is water vapor |
As an example, a wet basis concentration of 40 ppmv in a gas having 10 volume percent water vapor would have a:
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: [8]
where: | |
Cr | = corrected concentration of a dry gas with a specified reference volume % O2 |
---|---|
Cm | = measured concentration in a dry gas having a measured volume % O2 |
As an example, a measured NOx concentration of 45 ppmv in a dry gas having 5 volume % O2 is:
when corrected to a dry gas having a specified reference O2 content of 3 volume %.
Note:
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: [8]
where: | |
Cr | = corrected concentration of a dry gas having a specified reference volume % CO2 |
---|---|
Cm | = measured concentration of a dry gas having a measured volume % CO2 |
As an example, a measured particulates concentration of 200 mg/m3 in a dry gas that has a measured 8 volume % CO2 is:
when corrected to a dry gas having a specified reference CO2 content of 12 volume %.
Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors which change the measured quantity value without changing its effects. Unit conversion is often easier within the metric or the SI than in others, due to the regular 10-base in all units and the prefixes that increase or decrease by 3 powers of 10 at a time.
The Mach number, often only Mach, is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound. It is named after the Austrian physicist and philosopher Ernst Mach.
In thermodynamics, the specific heat capacity of a substance is the heat capacity of a sample of the substance divided by the mass of the sample, also sometimes referred to as massic heat capacity or as the specific heat. Informally, it is the amount of heat that must be added to one unit of mass of the substance in order to cause an increase of one unit in temperature. The SI unit of specific heat capacity is joule per kelvin per kilogram, J⋅kg−1⋅K−1. For example, the heat required to raise the temperature of 1 kg of water by 1 K is 4184 joules, so the specific heat capacity of water is 4184 J⋅kg−1⋅K−1.
Relative density, sometimes called specific gravity, is a dimensionless quantity defined as the ratio of the density of a substance to the density of a given reference material. Specific gravity for liquids is nearly always measured with respect to water at its densest ; for gases, the reference is air at room temperature. The term "relative density" is often preferred in scientific usage, whereas the term "specific gravity" is deprecated.
The troposphere is the lowest layer of the atmosphere of Earth. It contains 75% of the total mass of the planetary atmosphere and 99% of the total mass of water vapor and aerosols, and is where most weather phenomena occur. From the planetary surface of the Earth, the average height of the troposphere is 18 km in the tropics; 17 km in the middle latitudes; and 6 km in the high latitudes of the polar regions in winter; thus the average height of the troposphere is 13 km.
In a mixture of gases, each constituent gas has a partial pressure which is the notional pressure of that constituent gas as if it alone occupied the entire volume of the original mixture at the same temperature. The total pressure of an ideal gas mixture is the sum of the partial pressures of the gases in the mixture.
Atmospheric pressure, also known as air pressure or barometric pressure, is the pressure within the atmosphere of Earth. The standard atmosphere is a unit of pressure defined as 101,325 Pa (1,013.25 hPa), which is equivalent to 1,013.25 millibars, 760 mm Hg, 29.9212 inches Hg, or 14.696 psi. The atm unit is roughly equivalent to the mean sea-level atmospheric pressure on Earth; that is, the Earth's atmospheric pressure at sea level is approximately 1 atm.
An aerosol is a suspension of fine solid particles or liquid droplets in air or another gas. Aerosols can be natural or anthropogenic. The term aerosol commonly refers to the particulate/air mixture, as opposed to the particulate matter alone. Examples of natural aerosols are fog or mist, dust, forest exudates, and geyser steam. Examples of anthropogenic aerosols include particulate air pollutants, mist from the discharge at hydroelectric dams, irrigation mist, perfume from atomizers, smoke, dust, steam from a kettle, sprayed pesticides, and medical treatments for respiratory illnesses. When a person inhales the contents of a vape pen or e-cigarette, they are inhaling an anthropogenic aerosol.
The Dobson unit (DU) is a unit of measurement of the amount of a trace gas in a vertical column through the Earth's atmosphere. It originated, and continues to be primarily used in respect to, atmospheric ozone, whose total column amount, usually termed "total ozone", and sometimes "column abundance", is dominated by the high concentrations of ozone in the stratospheric ozone layer.
The speed of sound is the distance travelled per unit of time by a sound wave as it propagates through an elastic medium. At 20 °C (68 °F), the speed of sound in air is about 343 metres per second, or one kilometre in 2.91 s or one mile in 4.69 s. It depends strongly on temperature as well as the medium through which a sound wave is propagating. At 0 °C (32 °F), the speed of sound in air is about 331 m/s. More simply, the speed of sound is how fast vibrations travel.
The density of air or atmospheric density, denoted ρ, is the mass per unit volume of Earth's atmosphere. Air density, like air pressure, decreases with increasing altitude. It also changes with variations in atmospheric pressure, temperature and humidity. At 101.325 kPa (abs) and 20 °C, air has a density of approximately 1.204 kg/m3 (0.0752 lb/cu ft), according to the International Standard Atmosphere (ISA). At 101.325 kPa (abs) and 15 °C (59 °F), air has a density of approximately 1.225 kg/m3 (0.0765 lb/cu ft), which is about 1⁄800 that of water, according to the International Standard Atmosphere (ISA). Pure liquid water is 1,000 kg/m3 (62 lb/cu ft).
In electrochemistry, the standard hydrogen electrode, is a redox electrode which forms the basis of the thermodynamic scale of oxidation-reduction potentials. Its absolute electrode potential is estimated to be 4.44 ± 0.02 V at 25 °C, but to form a basis for comparison with all other electrochemical reactions, hydrogen's standard electrode potential is declared to be zero volts at any temperature. Potentials of all other electrodes are compared with that of the standard hydrogen electrode at the same temperature.
The true airspeed of an aircraft is the speed of the aircraft relative to the air mass through which it is flying. The true airspeed is important information for accurate navigation of an aircraft. Traditionally it is measured using an analogue TAS indicator, but as the Global Positioning System has become available for civilian use, the importance of such air-measuring instruments has decreased. Since indicated, as opposed to true, airspeed is a better indicator of margin above the stall, true airspeed is not used for controlling the aircraft; for these purposes the indicated airspeed – IAS or KIAS – is used. However, since indicated airspeed only shows true speed through the air at standard sea level pressure and temperature, a TAS meter is necessary for navigation purposes at cruising altitude in less dense air. The IAS meter reads very nearly the TAS at lower altitude and at lower speed. On jet airliners the TAS meter is usually hidden at speeds below 200 knots (370 km/h). Neither provides for accurate speed over the ground, since surface winds or winds aloft are not taken into account.
The number density is an intensive quantity used to describe the degree of concentration of countable objects in physical space: three-dimensional volumetric number density, two-dimensional areal number density, or one-dimensional linear number density. Population density is an example of areal number density. The term number concentration is sometimes used in chemistry for the same quantity, particularly when comparing with other concentrations.
In physics, a mass balance, also called a material balance, is an application of conservation of mass to the analysis of physical systems. By accounting for material entering and leaving a system, mass flows can be identified which might have been unknown, or difficult to measure without this technique. The exact conservation law used in the analysis of the system depends on the context of the problem, but all revolve around mass conservation, i.e., that matter cannot disappear or be created spontaneously.
The wet-bulb temperature (WBT) is the temperature read by a thermometer covered in water-soaked cloth over which air is passed. At 100% relative humidity, the wet-bulb temperature is equal to the air temperature ; at lower humidity the wet-bulb temperature is lower than dry-bulb temperature because of evaporative cooling.
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.
The hypsometric equation, also known as the thickness equation, relates an atmospheric pressure ratio to the equivalent thickness of an atmospheric layer considering the layer mean of virtual temperature, gravity, and occasionally wind. It is derived from the hydrostatic equation and the ideal gas law.
In respiratory physiology, airway resistance is the resistance of the respiratory tract to airflow during inhalation and exhalation. Airway resistance can be measured using plethysmography.
The liquid water content (LWC) is the measure of the mass of the water in a cloud in a specified amount of dry air. It is typically measured per volume of air (g/m3) or mass of air (g/kg). This variable is important in figuring out which types of clouds are likely to form and is strongly linked to three other cloud microphysical variables: the cloud drop effective radius, the cloud drop number concentration, and the cloud drop size distribution. Being able to determine the cloud formations that are likely to occur is extremely useful for weather forecasting as cumulonimbus clouds are related to thunderstorms and heavy rain whereas cirrus clouds are not directly associated with precipitation.
This article incorporates material from the Citizendium article "Air pollutant concentrations", which is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License but not under the GFDL.