Calculate Air Quality Near a Chimney

Nature is a complex process. Humans have tried to simplify this complex process to a model, mostly making many assumptions. The dispersion of pollutants in the air is also a complex process, and multiple factors determine their behavior.

Several models have been developed and are still developing to predict the natural process better. With better technology and computational power, we will go towards predicting the nature with better accuracy.

CLICK: EXCEL DESIGN SHEET (CALCULATE)

The Gaussian dispersion model has been in use for many decades for its simplicity in regulating and monitoring pollution.

The Gaussian dispersion model has assumptions as:

• Emission and meteorological conditions remain constant
• No chemical transformation occurs
• Wind speeds are always equal to or greater than 1 m/s

According to the World Health Organization, the maximum level of SO2 concentration at ground level is 40 micrograms per cubic meter over a 24-hour average (SOURCE).

The height of the chimney should be high enough to limit the ground-level concentration of pollutants. Otherwise, engineering methods to limit the pollutants should be adopted.

PM_2.5 and SO₂ are much higher than other pollutants in an industrial area. Hence, designing a safe system for PM_2.5 and SO₂ will also cover other pollutants gases.

The Gaussian plume model is a widely accepted model for the dispersion of pollutants in air, whose general equation is:

• C = Concentration of Pollutant ( gram/m₃)
• Q = Pollution emission rate (g/s)
• u = mean wind speed at stack height (m/s)
• H = Effective height of Stack, also H_e (m)
• σ_y = Plume’s standard deviation in cross-wind direction (m): Given by Chart
• σ_z = Plume’s standard deviation in the vertical direction (m): Given by Chart
• z = Level of computation of concentration (m)
• x,y = Down-wind and cross-wind direction (m)

From the above equation, to determine the ground level concentration in the center of the plume, the z should be zero i.e. z=0, then the equation becomes:

The above equation will be maximum (i.e. the maximum pollution concentration) occurs when the ratio of σz to H is 0.707 where σz/σy is constant with x.

Hence, ΔC will be maximum at σz = 0.707 H,

where H is effective height (chimney height + height of plume)

Again, considering the condition of burning at the ground level without any chimney, the equation becomes simple as:

Now, with all the information, we can easily know the concentration anywhere from the emission source.

The standard deviation in the y and z directions is already modeled for different stability types of atmospheric turbulence. It is classified into six types from extremely stable atmosphere (Type A) to moderately stable types (Type F) by Pasquill-Gifford.

Type A: The atmosphere is extremely stable which gives the highest pollution concentration

Type F: The atmosphere is moderately stable which gives the lowest pollution concentration

Pasquill-Gifford gives the dispersion coefficient in the form of charts:

The use of charts to solve the equation is tedious. Hence, several formulas have been developed to best fit the curve. The equation below is the simplest one, which fits the charts.

Now, with all the known information, the concentration of pollutants can be known anywhere across 3-dimensions of the space. The location where the maximum concentration occurs is also known.

Now, let’s look at the example to understand it better.

……

EXAMPLE 1: AIR POLLUTION FROM AN EXISTING INDUSTRY

What will be the maximum pollution concentration at ground level and where will be the maximum concentration of a powerplant that burns 5 tons of coal per hour and releases smoke with a stack of effective height of 70 meters? The coal has a sulfur content of 4.2 percent. The wind velocity at the top of the stack is 6.0 m/s and the atmospheric condition is slightly stable (Class C). What will the pollution be at a home that is just 300 meters away from the chimney?

SOLUTION:

Maximum Pollution concentration = ?

Location of maximum pollution = ?

Pollution at nearby house = ?

Now,

Hence, the minimum height of the chimney required for the safe dispersion of pollutant gases is ~86 meters. So, the chimney of a height below 70 meters is faulty.

However, if the pollution concentration can be within the WHO limits, the existing height will be safe even if it doesn’t comply with the standard norms.

Hence, now let’s calculate the pollution concentrations. According to Gaussian plume distribution, the maximum level of concentration occurs at a distance of:

σ_z = 0.707 H_e = 0.707 * 75 = 53.03 meter, which corresponds for class C from the solution table as:

σ_z = a (x)^b

53.03 = 0.112960 (x)^0.9102

On solving, we get (Distance from point source where maximum pollutant concentration occurs (x) = 861 meters

In all other locations near or far, the pollution concentration will be lesser than that

The maximum concentration will be:

Emission of SO₂ (Q) = 116.66 gram/second

Wind velocity (u) = 6 m/s

Effective Height of Chimney (H_e) = 75 meter

σ_z = 53.03 meter

σ_y = a (x)^b =0.219 (861)^0.8949 = 92.68 meter

Concentration (C) = 0.000306 gram/Cubic meter

Thus, Concentration of SO₂ (C) = 306 µg/m³

This concentration exceeds the maximum allowable ground level concentration recommended by WHO for SO₂ as 40 µg/m3.

Note: An average concentration over 24 hours recommended by WHO is 40 µg/m3, whereas the average concentration over 10 minutes recommended by WHO is 500 µg/m3 (SOURCE)

Thus, measures must be taken to control air pollution. The possible steps can be:

• Engineering measures for air pollution control
• Lower the capacity of the industry
• Use a better fuel
• Increase the height of the chimney

Let’s also know the concentration at the house in the direction of the smoke plume at a location of 300 meters from the chimney:

σ_z = a (x)^b = 0.112960 (300)^0.9102 = 20.3 meter

σ_y = a (x)^b =0.219 (300)^0.8949 = 36.1 meter

Concentration of SO₂ at 300 meter (C_300,0,0 ) = 210 µg/m³

Still, the concentration at the house far exceeds the safe limits. Note that, the house falls directly in the direction of the plume of smoke. For smoke traveling in another direction, the concentration can be calculated which will be lesser.

……

EXAMPLE 2: DESIGN A NEW CHIMNEY AND CHECK FOR AIR POLLUTION

A new chimney is to be designed for an 8 ton capacity boiler using rice husk as a fuel such that it follows all the guidelines which also keeps the maximum pollution within the WHO limit.

The provided data for Fuel are as:

• Fuel Used is Rice Husk
• Fuel feed rate = 2400 kg/hr for 8-ton boiler capacity (SOURCE)
• Total Particulate Matter (PM) released = 36.9 g/kg of Rice husk burned (SOURCE)
• Total Particulate Matter (PM2.5) released = 3.9 g/kg of Rice husk burned (SOURCE)
• Total Particulate Matter (PM10) released = 9.5 g/kg of Rice husk burned (SOURCE)

Other Data’s are:

• V_s = 11.5 m/s
• u = 6 m/s
• d = 1.00 m
• p = 1000 millibars
• T_s = 150 Degree Celsius = (273+150) Degree Celsius = 423 Degree Celsius
• Ta = 20 Degree Celsius = (273+20) Degree Celsius = 293 Degree Celsius

1 . Chimney height designed for Particulate matter:

Since particles greater than 10 microns are larger particles and need to be settled at site. The chimney should thus be designed for PM₁₀. Also, the SO2 emission for fuel using Rice husk is low and hence can be ignored.

Particulate matter emission (Qp) = 2400*9.5/1000000 = 0.0228 ton/hour

H = 74 (Qp)^0.27 = = 74 (0.0228)^0.27 = 26.66 meter

Minimum Height of Chimney = 26.66 meters (for Particulate Matter)

However, the minimum height of a chimney for this type of industry is 30 meters. Keeping the chimney height at 30 meters is okay.

So, Height of Chimney = 30 meters.

2 . Height of the Smoke Plume

• Height of the smoke plume (Δ h) = Needed to be calculated?

Hollands equation is often used for the determination of the plume height from chimneys,

• Δ h = Plume height (meter)
• V_s = Stack exit velocity (m/s)
• u = wind speed (m/s)
• d = diameter of stack at exit (m)
• p = atmospheric pressure in millibars
• T_s = Stack gas temperature (Degree Kelvin)
• Ta = Air temperature (Degree Kelvin)

Using Holland’s equation,

Plume height (Δ h) = 4.45 meter

The effective height of the stack is (H_e) = h + Δ h = 30 + 4.45 = 34.45 meters

Hence, the smoke will plume/trail at 34.45 meters from the ground level.

3 . Maximum Concentration of Pollution at Ground Level

According to Gaussian plume distribution, the maximum level of concentration occurs at a distance of:

σ_z = 0.707 H_e = 0.707 * 34.45 = 24.36 meter,

The atmospheric condition for design is taken as neutral atmosphere which is described as Class D.

Note: More the stable the atmospheric condition, the more will be the concentration of pollutants.

Using the solution for Pasquill chart for Class F

σ_z = a (x)^b

24.36 = 0.268600 (x)^0.6597

On solving, we get (Distance from point source where maximum pollutant concentration occurs (x) = 937 meters

In all other locations near or far, the pollution concentration will be lesser than that

The maximum concentration will be:

Emission of PM₁₀ (Q) = 0.0228 ton/hour = 6.333 gram/second

Wind velocity (u) = 6 m/s

Effective Height of Chimney (H_e) = 34.45 meter

σ_z = 24.36 meter

σ_y = a (x)^b = 0.1323(937)^0.8998 = 62.45 meter

Concentration (C) = 0.0000403 gram/Cubic meter

Thus, Concentration of SO₂ (C) = 40.3 µg/m³

The WHO recommends that PM10 concentrations should not exceed 45 µg/m3 as a 24-hour average. Hence, the maximum concentration at the ground level of 40.3 µg/m³ is within the limits for concentration.

Conclusion: A chimney of 30 meters physical height of 1 meter diameter for an industry having a boiler capacity of 8 tons is sufficient for its height regulations and WHO regulations for Pollution.

……

Predicting natural processes with a hundred percent accuracy is not possible. With engineering measures, we model natural conditions that meet our desired accuracy for results. Thus, the design of the stack/chimney is complete as per conventional guidelines and regulations.

Also Read: Simple Height calculation of Chimney for industries (Part 1)

Also Read: Calculate the Rise of Smoke from a Chimney (Part 2)

SOURCES:

• Gaussian Plume Model Design of Effective Stack Hight For
  Control of Industrial Emissions
• MATHEMATICAL MODELING OF AIR POLLUTION IN A THERMAL POWER PROJECT: A PhD Thesis
• Atmospheric dispersion of pollution:F. Pasquill,1971
• USER’S GUIDE FOR THE INDUSTRIAL SOURCE COMPLEX (ISC3) DISPERSION MODELS