In this post, I want to share with you how to estimate effective stack height for disposing plant gases and vapors.
Estimating effective stack height for disposing plant gases and vapors is a critical task in chemical and process plant engineering. Improper stack design can lead to unsafe ground-level concentrations, explosion hazards, environmental non-compliance, and legal exposure. Effective stack height is defined as the sum of the physical stack height and the plume rise, ensuring that atmospheric contaminants are appropriately dispersed.
Regulatory Basis and Engineering Standards
Stack height is determined using engineering standards and regulations, including NFPA LEL criteria, air-quality rules from environmental agencies, and dispersion models like Bosanquet–Pearson.
Understanding Effective Stack Height
Effective stack height equals the physical stack height plus the added plume rise from exit velocity and buoyancy.
These are general guide for stack design:
- The concentration of an effluent measured downwind from its source is directly proportional to the volume discharged.
- Material dilution of the effluent does not significantly alter the downwind ground-level contaminant concentration.
- Downwind concentrations decrease as wind speed increases; specifically, doubling the wind speed will halve the pollutant concentration.
- Pollutant concentration at ground level is inversely proportional to the square of the stack height, so doubling the height reduces the maximum concentration to one quarter of its original value.
- The position of the maximum ground-level concentration is influenced by atmospheric stability. Under unstable conditions—such as during high wind speeds or temperature inversions—the peak concentration occurs closer to the stack. As wind speed further increases and inversions dissipate, this peak concentration shifts farther from the source.
Step-by-Step Estimation Method and Example
The estimation process begins with converting emission flow rate into molar units using molecular weight. The allowable downwind concentration is typically defined as 25–40 percent of the LEL for flammable gases. Using empirical dispersion charts or equations, engineers then determine the minimum effective stack height that maintains concentrations below allowable limits.
Example
Acetylene, which has a molecular weight of 26, is released from a process at a rate of 100 lb/min. What stack height is required to ensure that the downwind concentration does not exceed 40% of its lower explosive limit, given that the LEL is 2.5?
Solutions
There are four steps used to estimate stack height for disposing plant gases and vapors.
- Compile the data
- Determine allowable concentration of vapor
- Estimate required stack height
- Estimate distance downwind of the stack
Data:
- Component = acetylene
- Emission rate = 100 lb/min
- Molecular weight = 26 lb/lbmol
Allowable concentration of vapor :
- Lower explosion limit (LEL) = 2.5%-v
- Allowable downwind concentration = 40% of LEL = 40% x 2.5% = 1%-v
Required stack height :
- Molar flow rate = mass flow/molecular weight = 100 lb/min / 25 lb/lbmol x 60 = 230 lbmol/hour
- Minimum stack height is estimated using graph below. Based on the graph, at 1%-v lower explosive limit and contaminant concentration 230 lbmol/hour, the minimum stack height is just below 25 ft. Let’s choose 25 ft as minimum stack height
Please be noted that the stack height is based on wind speed 1 mi/h (1.6 km/h) and the ratio of vertical diffusion coefficient and horizontal diffusion coefficient is 1.
Distance downwind of the stack:
The distance downwind of the stack is the function of turbulence condition. The location downwind from the stack at which the maximum concentration occurs is influenced by turbulence conditions within the surrounding area. Turbulence parameters, as detailed in the Bosanquet-Pearson study, are outlined below:
- p (Vertical Turbulence Parameter): Represents the coefficient of vertical diffusion. It determines how quickly the plume expands in height as it moves downwind.
- q (Horizontal Turbulence Parameter): Represents the coefficient of horizontal diffusion, dictating the lateral “widening” of the smoke or gas cloud
The distance downwind from the stack for maximum concentration of the effluent is estimated by using the following equation :
d = H/(2 x p)
d = distance downwind from the stack for maximum concentration of the effluent (ft)
H = stack height (ft)
p = vertical diffusion coefficient
Therefore, for moderate turbulence, the distance downwind from the stack for maximum concentration of the effluent = 25 / (2 x 0.50) = 250 ft.
Free Spreadsheet
You can download free spreadsheet on how to estimate stack height for disposing plant gases and vapors below.
Free spreadsheet on how to estimate stack height for disposing plant gases and vapors.
I hope you find this simple post useful.
Reference:
- Hicks, Tyler G. Standard Handbook of Engineering Calculations Fourth Edition. McGraw-Hill Standard Handbooks