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Estimating CO2

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Kinetics and more than you need to know (more than you want to know?)

I have written that carbon monoxide, CO, disperses 25 percent faster than carbon dioxide, CO2. That should be documented.

From Mr. Maxwell and kinetics we know that gas molecules are very fast. This may be used to convince you that emissions will not be around long. Be prepared with the proper perspective, so 'the suits' can't snocker you.

Since writing this, I have discovered more things such as the most probable velocity and mean velocity, both of which are a bit slower than the rms one. I don't think it will change much of the analysis, but I will try to incorporate them, eventually.

Indeed, CO2 will have a root-mean-square molecular speed, rms, of around 1,112 miles per hour when it leaves Nippon’s proposed biomass boiler at 325.4 degrees Fahrenheit (163 degrees Centigrade/Celsius, or 436 degrees Kelvin, source: Nippon’s revised submission to ORCAA, page 5-3). That doesn’t mean those molecules will be 1,112 miles away in one hour --- far from it. They will slow down as they enter the more cool air. At 32 degrees Fahrenheit (0 degrees Celsius/Centigrade, or 273 degrees Kelvin), their rms will be 880 miles per hour. And, probably not one molecule will even be 880 miles away either. The reason is that rms is not like any speed you are familiar with.

It does help that the emissions will be ejected upwards from the top of the smokestack (38.1 meters or 125 feet off the ground) at a velocity of 9.97 meters per second (22.3 miles per hour).

If you have studied electricity, you may have seen an oscilloscope display of alternating current. The current changes directions. The gas molecules do likewise. They are constantly running into other CO2 molecules and a whole bunch of oxygen molecules and even more nitrogen ones plus other stuff such as water molecules and particulates.

Imagine a hundred blind men without any arms and no ability to sense each other gathered around the 50-yard line at a football field, facing in random directions. However, they are able to know when you give them the signal to run as fast as they can away from their current positions. Add some more obstacles for them.

Of course the gas molecules don’t fall down in a heap; they bounce right off and keep going. They constantly ricochet off stuff, and stuff constantly runs into them. Think of the rms as an average, kind of.

Here is a formula you can use to calculate the rms, designated as ‘u.’

‘C’ is the temperature in degrees Centigrade or Celsius, which we convert to degrees Kelvin by adding 273. The answer will be in meters per second. I have left out all the units associated with the numbers to make it easy. I have also simplified the numbers.

u = (24,930 x (273 + C)/Atomic weight of gas molecule)^(1/2)

The ^(1/2) means that you take the square root of the previous stuff.

To convert to miles per hour, multiply by 3,600 seconds/hour and divide by 1,609.344 meters/mile.

Monoxide is 25.4 percent faster at all temperatures. Check it out. (Atomic weight CO2 = 44, CO = 28).

Now, for some perspective:

Please forgive me for being crude, but this is something I think everyone can relate to. A ‘girly’ fart is mostly methane, CH4, atomic weight = 16. An ‘ogre-man’ fart (imagine beer, potato chips, boiled eggs, etcetera prior) contains a lot of hydrogen sulfide, H2S, atomic weight = 34. There is a considerable difference in how long the odors remain even though the rmsesses for both are high. At 98.6 degrees Fahrenheight, 1,555 and 1,067 mph, respectively.

Methane is 46 percent faster than hydrogen sulfide, and hydrogen sulfide is 13.8 percent faster than CO2 at the same temperature. Major ‘hang time?’

Some additional perspective:

If you are in a room with two others, across the room next to each other, and one of them farts, and the non-farting one sounds the alarm, you have time to runaway before the odor reaches you, provided the other two aren’t between you and the only exit. In fact, you have time to walk away from it despite the rms. And, remember CO2 is slower.

The air in the room is still. Sometimes the outside air is still. That is when the emissions cause a problem. The wind is more important than kinetics, at least early after the release.

Fortunately, CO2 has no odor. Fortunately, a fart ends. The CO2 doesn’t.

What about a 436 degree Kelvin fart?

As a minimum, someone will need new underwear!

Quiz: How fast is a ‘girly-man’ fart?

Answer: Not fast enough!

Some afterthoughts ---

I recall reading an old warning that CO2 "does not readily disperse." It tends to seek low areas and displaces the oxygen there. It was commonly used in fire extinguishers (It is amazing to me that such extinguishers have disappeared. Ask a firefighter about them and see the reaction). I would be remiss if I did not disclose that such CO2 (as a gas escaping from a relatively small opening in a cylinder) was much colder. The cold also helped in fighting the fire, but the big thing was the actual CO2 level. Even if there were enough oxygen left to support combustion, once the CO2 level reached about 4 percent, 40,000 ppm, the fire would go out. Of course that level could present a threat to the firefighter too. We are not facing that kind of threat from emissions, but we are threatened. The fish in Hood Canal are facing such a threat from the CO2 produced by the algae.

I don't think gravity is considered in kinetics. I have an image of a pin ball machine in mind. The balls bounce and ricochet as they work their way down the playing surface. The gas molecules don't have the mass of the pin balls, but if you have seen the "smoke" from dry ice, frozen CO2, obviously gravity is involved. The remark that CO2 tends to seek low areas sticks in my head.

From our home, which had a territorial view of Puget Sound and the Olympic Mountains, we watched the difference in the appearance of the air as emissions changed. The old brown haze, which reached high into the sky did disappear. It had been spread out fairly consistently but was slightly thicker near the ground. When the new emissions were visible (granted, not as often), they were yellowish and did not reach high into the sky. They were concentrated near the ground. The new molecules were heavier. Air is a medium of transport. We should optimize its ability to carry the pollution out to the trees and oceans, and not hinder it. Ask yourself why our ancestors wanted our public buildings to have high ceilings.

The next thing I observed was that I could no longer smell the fragrances in the evening air when I went outside. I was a fortunate one --- many others began to have serious allergy problems and even asthma. There began an epidemic.

Something like 80 to 90 percent of the atmosphere is within 10 to 20 kilometers of the earth. That wouldn't be so if only kinetics were involved, would it?

I also recollect an episode of "Ask Mr. Wizard" in which Don Herbert experimented with CO2. In an aquarium, he had placed a small staircase. On each step was a burning candle. A couple feet above the aquarium, he released CO2. I don't recall exactly that part. I have a recollection from somewhere that CO2, though a gas, pours like a liquid. I trust Mr. Wizard's method of release would not compromise the experiment. Perhaps he poured the CO2 from a bottle. (Remember, it is invisible). Soon the candle on the bottom step went out, then the next one up, etcetera. The CO2 gas was filling the aquarium from the bottom up just as a liquid would. In order to put out the candle, the CO2 had to displace the air in the aquarium. It could do that because it was heavier than air, about 50 percent heavier.

My college chemistry textbook (King and Caldwell) told about a cave in Italy into which a man went walking with his little dog. Mistake. The CO2 accumulation near the floor killed the dog; the man was not harmed.

The old miners, so the story goes, had, in addition to a canary, two lamps. One was placed near the floor; the other up high. If the one on the floor grew dim or went out, the danger was from CO2. If the one up high grew brighter, the danger was from methane. I guess if the canary croaked, but the lamps didn't show anything, the danger was from carbon monoxide --- although carbon monoxide is also lighter than air like methane and does burn. You decide.

My brain tells me that 25 percent is not enough to add for CO2, but it will have to do for now.

Copyright © 2010 Donald L. Beeman. All rights reserved.