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. [1]

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:

and for the reverse conversion:

where: 
ppmv= air pollutant concentration, in parts per million by volume
mg/m3= milligrams of pollutant per cubic meter of air
= atmospheric temperature in kelvins = 273.15 + °C
0.08205= Universal Gas Law constant in atm·l/(mol·K)
= molecular weight of the air pollutant (dimensionless)

Notes:

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: [2]

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:

where: 
= altitude, in hundreds of meters
= atmospheric pressure at altitude , in atmospheres
= Concentration at sea level altitude, in mass per unit volume
= Concentration at altitude , in mass per unit volume

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:

Wind speed conversion factors

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

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:

Correcting for reference conditions

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 O2. 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 CO2.

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

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: [3]

where: 
= 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

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: [4]

where: 
= corrected concentration in a dry gas having a specified reference volume % O2 =
= measured concentration in a dry gas having a measured volume % O2 =

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: [5]

where: 
= corrected concentration in a dry gas having a specified reference volume % CO2 =
= measured concentration in a dry gas having a measured volume % CO2 =

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:

See also

Related Research Articles

Conversion of units is the conversion of the unit of measurement in which a quantity is expressed, typically through a multiplicative conversion factor that changes the unit without changing the quantity. This is also often loosely taken to include replacement of a quantity with a corresponding quantity that describes the same physical property.

<span class="mw-page-title-main">Mach number</span> Ratio of speed of an object moving through fluid and local speed of sound

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 Czech physicist and philosopher Ernst Mach.

<span class="mw-page-title-main">Specific heat capacity</span> Heat required to increase temperature of a given unit of mass of a substance

In thermodynamics, the specific heat capacity of a substance 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. It is also referred to as massic heat capacity or as the specific heat. More formally it is the heat capacity of a sample of the substance divided by the mass of the sample. 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.

<span class="mw-page-title-main">Relative density</span> Ratio of two densities

Relative density, also 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 preferred in SI, whereas the term "specific gravity" is gradually being abandoned.

<span class="mw-page-title-main">Troposphere</span> Lowest layer of Earths atmosphere

The troposphere is the lowest layer of the atmosphere of Earth. It contains 80% 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.

<span class="mw-page-title-main">Partial pressure</span> Pressure of a component gas in a mixture

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.

<span class="mw-page-title-main">Aerosol</span> Suspension of fine solid particles or liquid droplets in air or another gas

An aerosol is a suspension of fine solid particles or liquid droplets in air or another gas. Aerosols can be generated from natural or human causes. The term aerosol commonly refers to the mixture of particulates in air, and not to the particulate matter alone. Examples of natural aerosols are fog, mist or dust. Examples of human caused aerosols include particulate air pollutants, mist from the discharge at hydroelectric dams, irrigation mist, perfume from atomizers, smoke, dust, sprayed pesticides, and medical treatments for respiratory illnesses.

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 by, and continues to be primarily used in respect to, the study of 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.

<span class="mw-page-title-main">Speed of sound</span> Speed of sound wave through elastic medium

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 m/s, or 1 km 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.

<span class="mw-page-title-main">Lapse rate</span> Vertical rate of change of temperature in atmosphere

The lapse rate is the rate at which an atmospheric variable, normally temperature in Earth's atmosphere, falls with altitude. Lapse rate arises from the word lapse, in the sense of a gradual fall. In dry air, the adiabatic lapse rate is 9.8 °C/km. The saturated adiabatic lapse rate (SALR), or moist adiabatic lapse rate (MALR), is the decrease in temperature of a parcel of water-saturated air that rises in the atmosphere. It varies with the temperature and pressure of the parcel and is often in the range 3.6 to 9.2 °C/km, as obtained from the International Civil Aviation Organization (ICAO). The environmental lapse rate is the decrease in temperature of air with altitude for a specific time and place. It can be highly variable between circumstances.

In physical chemistry, Henry's law is a gas law that states that the amount of dissolved gas in a liquid is directly proportional to its partial pressure above the liquid. The proportionality factor is called Henry's law constant. It was formulated by the English chemist William Henry, who studied the topic in the early 19th century. In simple words, we can say that the partial pressure of a gas in vapour phase is directly proportional to the mole fraction of a gas in solution.

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.

<span class="mw-page-title-main">Atmospheric dispersion modeling</span> Mathematical simulation of how air pollutants disperse in the ambient atmosphere

Atmospheric dispersion modeling is the mathematical simulation of how air pollutants disperse in the ambient atmosphere. It is performed with computer programs that include algorithms to solve the mathematical equations that govern the pollutant dispersion. The dispersion models are used to estimate the downwind ambient concentration of air pollutants or toxins emitted from sources such as industrial plants, vehicular traffic or accidental chemical releases. They can also be used to predict future concentrations under specific scenarios. Therefore, they are the dominant type of model used in air quality policy making. They are most useful for pollutants that are dispersed over large distances and that may react in the atmosphere. For pollutants that have a very high spatio-temporal variability and for epidemiological studies statistical land-use regression models are also used.

<span class="mw-page-title-main">Wet-bulb temperature</span> Temperature read by a thermometer covered in water-soaked cloth

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.

Accidental release source terms are the mathematical equations that quantify the flow rate at which accidental releases of liquid or gaseous pollutants into the ambient environment which can occur at industrial facilities such as petroleum refineries, petrochemical plants, natural gas processing plants, oil and gas transportation pipelines, chemical plants, and many other industrial activities. Governmental regulations in many countries require that the probability of such accidental releases be analyzed and their quantitative impact upon the environment and human health be determined so that mitigating steps can be planned and implemented.

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.

Turbulent diffusion is the transport of mass, heat, or momentum within a system due to random and chaotic time dependent motions. It occurs when turbulent fluid systems reach critical conditions in response to shear flow, which results from a combination of steep concentration gradients, density gradients, and high velocities. It occurs much more rapidly than molecular diffusion and is therefore extremely important for problems concerning mixing and transport in systems dealing with combustion, contaminants, dissolved oxygen, and solutions in industry. In these fields, turbulent diffusion acts as an excellent process for quickly reducing the concentrations of a species in a fluid or environment, in cases where this is needed for rapid mixing during processing, or rapid pollutant or contaminant reduction for safety.

<span class="mw-page-title-main">Air pollutant concentrations</span>

Air pollutant concentrations, as measured or as calculated by air pollution dispersion modeling, 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 environmental protection and occupational health and safety agencies.

The residence time of a fluid parcel is the total time that the parcel has spent inside a control volume (e.g.: a chemical reactor, a lake, a human body). The residence time of a set of parcels is quantified in terms of the frequency distribution of the residence time in the set, which is known as residence time distribution (RTD), or in terms of its average, known as mean residence time.

References

  1. Air Dispersion Modeling Conversions and Formulas
  2. Beychok, Milton R. (2005). Fundamentals Of Stack Gas Dispersion (4th ed.). author-published. ISBN   0-9644588-0-2.
  3. 40 U.S. Code of Federal Regulations, Chapter I, Part 60, Appendix A-3, Test Method 4.
  4. 40 U.S. Code of Federal Regulations, Chapter I, Part 60, Appendix B, Performance Specification 2.
  5. 40 U.S. Code of Federal Regulations, Chapter I, Part 60.