Suppose you want to estimate the combustion products from heaters, boilers, etc. Based on my experience, the environmental specialist doing the Gaussian distribution calculation needs the following needs the four pieces of information about the combustion equipment. Below, I list them, and suggest where you might find them:
- Amount of exhaust gas/complete combustion products: get by vendor quote, or by combustion equation (see below), or Combustion rules of thumb
- Amount of contaminates/incomplete combustion products: get by vendor quote or by the US EPA’s guideline AP 42
- Gas Discharge velocity: exhaust gas volume ÷ stack area (using stack diameter from vendor quote)
- Likely site location and weather conditions: from plot plan & site climate data. (Wind modeling / testing may be required in some cases)
You’ll notice I said “vendor quote” a lot – that’s the best source if you’ve got it. If not, time to look up similar results and ask around and do some digging.
Combustion Equation
Suppose you have a fuel source made up of some mixture of hydrocarbons and other molecules. You want to calculate the amount of exhaust gas your heater will exhaust by burning it. For simple fuels, you can do this manually.
But what's coming out the stack? (Photo credit: William Warby)
First, look up the chemical composition of the fuel you are combusting. Then, knowing your composition and the LHV of each chemical in your composition, determine the overall lower heating value per amount of fuel you combust. Then, look at your heater’s duty ÷ heater efficiency, and calculate the amount of fuel you will be burning in the heater. If you don’t know the heater efficiency yet, look into industry literature for an estimate.
Then, knowing the chemical composition of your fuel and how much fuel you must burn overall, figure out how many moles of each chemical species you will be burning.
For any mole of hydrocarbon of chemical formula CxHy, with e excess air (where 1 is 100% excess air and 0.03 is 3% excess air), using air which we will approximate as 79% N2 / 21% O2, and assuming 100% complete combustion as a first approximation, we have this reaction formula:
CxHy + (1+e)(x+y/4)O2 + (1+e)(79/21)(x+y/4)N2 –> xCO2 + (y/2)H2O + eO2 + (1+e)(79/21)(x+y/4)N2
So for example ethane is C2H6, so substitute x=2 and y = 6 above. You are providing the perfect amount of oxygen for the combustion, and e% extra on top to help ensure complete combustion. The N2 is from the air and just goes along for the ride.
The CxHy equation also works for Hydrogen, just set x = 0.
For a mole of H2S:
H2S + (1+e)(3/2)O2 + (1+e)(79/21)(3/2)N2 –> SO2 + H2O + eH2O + (1+e)(79/21)(3/2)N2
For moles of N2, O2, CO2, H2O, assume no reaction and it passes through unchanged.
Repeat the calculation for each chemical you combust, and multiply the equations by the total number of moles of each chemical you combust. Then total up the products in a final tally. That’s a decent first approximation.
Complications
What if you have a complex fuel, like a heavy fuel oil with many chemical compounds? Or municipal waste of varying and uncertain contents? Then you can’t use the combustion method because you don’t know the composition precisely. I suggest you find some correlation or operating experience to make the best guess you can.
What about incomplete combustion products? It’s not feasible to predict these from first principles calculations. It is far too dependent on the geometry of the heater/boiler.). Realistically, you need information from expert vendors, or from very similar cases. AP 42 can give you an average value.
Weather conditions
Normally these will come the client in any project you work on. If you have to work from nothing, time to do some digging. One good step is to see if there are nearby weather stations – perhaps the one associated with an airport? You can get historical data on these for free. Another option might be if any wind surveys were done in the area, perhaps with an eye to building wind power.
Bonus
Check out Air dispersion equations and book
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