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

Representation of Gaussian Plume Model (SOURCE)

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).

*Air Quality Guidelines (AQG) of WHO (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:

*Figure: Vertical Dispersion Coefficient σ_y* (*Source*)

*Figure: Horizontal Dispersion Coefficient σ_z* (*Source*)

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.

*Table: Solution for Pasquill-Gifford chart for dispersion coefficient* (SOURCE)

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,

Solution:

Emission rate of Sulphur = 5*1000*0.042 = 231 kg/hour

Sulfur in coal combines with oxygen to form SO₂,

S ( 210Kg ) + O2 ( 210Kg ) ———–> SO₂ (420Kg )

Emission rate of SO₂ (Qs) = 420 Kg/hour = 128.33 gram/second

Minimum Height of Chimney required = 14 (Qs)^0.3 = 14 (420)^0.3 = 85.7 meters

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)

Frequently Asked Questions (FAQ)

1. What is the Gaussian plume model for air quality calculation?

The Gaussian plume model is a widely used dispersion model that estimates local pollution levels based on factors like wind speed, wind direction, local terrain, and atmospheric turbulence intensity [1, 2]. It predicts pollutant concentrations at specific downwind locations.

2. What is the maximum safe SO₂ concentration at ground level?

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 [3].

3. What are Pasquill-Gifford stability classes?

Atmospheric conditions are classified into six types from Type A (very unstable atmosphere with vigorous diffusion) to Type F (very stable with weak diffusion) [4, 5]. These classes determine dispersion coefficients used in the Gaussian model.

4. What parameters are needed to calculate ground-level concentration?

Required inputs include meteorological conditions like wind speed and direction, atmospheric turbulence, ambient temperature, emission rate, stack height, exit velocity, and terrain elevations [1, 6].

5. How do I calculate pollution concentration at a specific distance from a chimney?

Use the Gaussian dispersion equation with emission rate (Q), wind speed (u), effective stack height (H), and dispersion coefficients (σy and σz) for the specific downwind distance and atmospheric stability class [2, 7].

6. What are dispersion coefficients σy and σz?

The parameters σy and σz are the standard deviations of Gaussian distributions indicating the plume spread in horizontal and vertical directions respectively, and they increase with distance from the source [2, 7].

7. At what distance does maximum ground-level concentration occur?

The plume from an elevated source like a chimney stack usually reaches ground level after a downwind distance equivalent to between 10 and 20 times the stack height [8]. Maximum concentration typically occurs within this range.

8. How does atmospheric stability affect pollutant concentration?

In stable atmospheric conditions (Category F), dispersion is minimal and plumes can remain close to ground. In unstable conditions (Category A), dispersion is better with lower ground-level concentrations [4, 5].

9. What is the role of wind speed in ground-level concentration?

Higher wind speeds dilute pollutants more effectively, reducing ground-level concentrations. Wind speed appears in the denominator of the Gaussian equation, so higher speeds result in lower concentrations [2, 7].

10. How accurate are Gaussian dispersion models?

Gaussian models have proven to be accurate within 20% at ground level at distances less than 1 km, and accurate within 40% for elevated emissions [9], though terrain and meteorological variations can affect accuracy.

11. Can the model predict concentration at any location in 3D space?

With all known information including dispersion coefficients, the concentration of pollutants can be calculated anywhere across 3-dimensions of space [2, 7], not just at ground level.

12. What is the difference between 1-hour and 24-hour average concentrations?

The Gaussian equation predicts 1-hour average pollutant concentration. For longer averaging periods, concentrations are typically lower [10] due to temporal variations in emissions and meteorology.

13. How does terrain elevation affect air quality calculations?

Terrain elevation must be accounted for in the z-axis calculations. The Digital Elevation Model represents height above sea level, so the chimney’s altitude must be used as a reference point [6] for accurate vertical distance measurements.

14. What monitoring equipment is needed to validate model predictions?

Dispersion modeling is used to predict concentrations, but models should be validated with actual air quality monitoring data at selected receptor locations to ensure compliance with standards [3, 9].

15. How do I determine if a chimney height is adequate for safe dispersion?

Calculate the maximum ground-level concentration using the Gaussian model. The chimney height is adequate if this concentration stays below regulatory limits like WHO standards [3]. If concentrations exceed limits, increase stack height or implement emission controls.

Sources:

More SOURCES:

Post Views: 1,249