Calculate the Rise of Smoke from a Chimney

Chimneys are made to safely release the smoke from the industry to disperse them into the air. However, the released smoke covers some additional height before it takes the form of a smoke plume.

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REFRESH

The various parameters which make the modeling of a plume complex include:

Exit velocity
Wind speed
Diameter of chimney at exit
Temperature of Plume

Air turbulence
Air quality
Air moisture
Terrain

Cumulative effects

Several mathematical models have been developed to develop the dispersion model. The popular one is that smoke follows Gaussian concentration distribution.

H is the effective height of the chimney
Δ h is the plume height
h is the physical height of the chimney

Plume height calculation: Holland Equation

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)

The above is for neutral conditions. The value for Δ h can be increased by 10 to 20% for unstable conditions and decreased by the same for stable conditions.

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Example 1: Determine the effective height of a stack (h), with the following parameters

The physical stack is 200 meters tall with 1.00 meters diameter
Wind velocity is 3.00 m/s
Air temperature is 20 degrees Celsius
Barometric pressure is 1000 millibars
Stack gas velocity is 11.5 m/s
Stack gas temperature is 150 degrees Celsius

SOLUTION:

Δ h = Needed to be calculated?
V_s = 11.5 m/s
u = 3 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

Using Holland’s equation,

Plume height (Δ h) = 8.90 meter

The effective height of the stack is (H) = h + Δ h = 200 + 8.9 = 208.9 meters

Hence, the smoke will plume/trail at 208.9 meters from the ground level.

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Example 2: Determine the Physical height of the Chimney and the smoke plume height with the following available data

Factory Capacity: 2400 tonnes of coal with a sulfur content of 4.2% burned per day
Diameter of the stack to be used = 8 meter
Gas exit velocity = 18.3 m/s
Temperature of gas released = 140 degrees Celsius
Ambient air temperature = 8 degrees Celsius
Atmospheric pressure = 1000 millibars
Average wind speed = 4.5 m/s

SOLUTION:

The physical height of the chimney = ?

The plume height = ?

The effective height of the chimney = ?

Using Holland’s equation

Plume height (Δ h) = 271.73 meter

Now, the physical height of the chimney is given by a formula prescribed by Indian standards as:

Physical height of chimney = 14 (Q_s))^0.3, where Q_s is SO₂ consumed in kg/hour

Let’s assume the factory runs for 12 hours daily, using 24000 tonnes of coal. Then,

Emission rate of Sulphur = 2400/12 *1000*0.042 = 8400 kg/hour

Sulfur in coal combines with oxygen to form SO₂,

S ( 8400 Kg ) + O2 ( 8400 Kg ) ———–> SO₂ (16800 Kg )

Emission rate of SO₂ (Qs) = 16800 Kg/hour

Minimum Height of Chimney required = 14 (Qs)^0.3 = 14 (16800)^0.3 = 259.3 meters

Hence, the minimum height of a physical chimney needs to be 260 meters.

The effective height of the Chimney will be (H) = 260 + 271.7 = 531.7 meter

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Now that we know the height to which the smoke rises, the next step is to determine its impact on air quality at ground level. Additionally, there will be a point where the smoke’s effect is most concentrated. To know this:

READ: “Calculate Air Quality Near a Chimney.” (Part 3)

To calculate the physical height of the Chimney required:

READ: “Simple Height calculation of Chimney for industries” (Part 1)

Frequently Asked Questions (FAQ)

1. What is plume rise in chimney emissions?

Plume rise is the vertical distance hot, buoyant gases travel above the physical top of a chimney due to momentum and thermal buoyancy [1]. This additional height is crucial for effective pollutant dispersion.

2. What is effective stack height and how is it calculated?

Effective stack height equals the physical stack height plus plume rise from buoyancy and momentum, minus any downwash effects [2]. It represents the actual altitude where pollutants disperse.

3. What factors contribute to plume rise?

Two main factors contribute to plume rise: thermal buoyancy from heated gases being warmer than ambient air, and initial vertical momentum from stack exit velocity [3]. Both increase the plume’s final height above the stack.

4. What are Briggs plume rise equations?

The Briggs equations, developed by G.A. Briggs between 1965-1972, are widely used formulas for calculating plume rise based on buoyancy flux, wind speed, and atmospheric stability [4]. They’re the industry standard for dispersion modeling.

5. How does wind speed affect plume rise?

Higher wind speeds bend the plume over more quickly, reducing the final plume rise height. A smoke plume takes on horizontal wind speed quickly but continues rising with vertical momentum and buoyancy [5].

6. What is buoyancy flux in plume rise calculations?

Buoyancy flux (F) represents the rate of heat emission from the stack, measured in m⁴/s³. It’s proportional to heat efflux and is a dominant term in predicting plume rise for buoyant plumes [6].

7. How does atmospheric stability affect smoke rise?

In stable atmospheric conditions, final plume rise is finite. In neutral conditions, rise is finite only with turbulence. In unstable conditions, rise can be finite or infinite depending on conditions [7].

8. What is the difference between plume rise and effective height?

Plume rise is only the additional vertical distance above the stack top, while effective stack height is the total height (physical stack + plume rise – downwash) [2].

9. What is stack downwash and how does it affect plume rise?

Stack downwash occurs when wake turbulence behind buildings or terrain pulls emissions downward, reducing effective stack height [8]. It significantly impacts ground-level pollution concentrations.

10. How is plume rise calculated for thermal power plants?

For power plants, Briggs equations for bent-over, hot buoyant plumes are most commonly used, as these plumes are dominated by buoyant momentum rather than initial velocity [4].

11. What meteorological data is needed for plume rise calculation?

You need wind speed at stack height, ambient temperature, atmospheric stability class, vertical temperature profile, and wind direction. Vertical profiles of wind and temperature are essential for accurate predictions [9].

12. Does chimney diameter affect plume rise?

Yes, larger stack diameters can affect the initial momentum and entrainment of ambient air into the plume, which influences the final rise height through the exit velocity relationship [3].

13. What is the typical plume rise for industrial chimneys?

Plume rise varies widely based on heat emission rates and conditions. At fixed distances with a 1-hour sampling period, significant regression lines relate plume rise to chimney gas heat emission [10], though scatter is considerable.

14. How does temperature difference affect plume rise?

The temperature difference between stack gases and ambient air directly affects buoyancy. Greater temperature differences produce more buoyancy, resulting in higher plume rise values [6].

15. Can plume rise be calculated for non-buoyant emissions?

Yes, but the calculations differ. For cold emissions without significant temperature difference, plume rise depends primarily on initial exit momentum rather than thermal buoyancy, requiring different formulas [3].

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