The table above managed to cause me about a month’s worth of confusion. Fucking table. The purpose of this blog entry is for those who hate English units, hate conversion factors of vague origins, or just hate a lot of things in general. Hate is the theme of this post. That and pollution. I hate pollution. Anyway, I hope the following post will save you the confusion it caused me. Acknowledgments to Jeremy Schreifels, who sent me lots of good resources for deciphering this mess.
China’s new air pollution standards went into effect on January 1, 2012. These new standards, much more strict than the previous ones established in 2003, are finally on par with the rest of the world (see above table). I’m in the business of sulfur dioxide standards, so I started staring at the table and comparing the U.S. standards to China’s. China’s standards are in mg/m3, i.e. milligrams of sulfur dioxide per cubic meter of flue gas. The U.S.’s standards are in lb/millionBtu(mmBtu), or pounds of sulfur dioxide per million Btu of coal. But if you look at the table, someone already did the dirty work and converted the U.S. units of lb/mmBtu into mg/m3. But for those of us who are analytical and shit, this was actually a disservice. I want to know where the numbers come from, dammit!
The conversion is not just your simple English-to-metric wahoo. The pounds-to-milligrams and cubic-feet-to-cubic-meter stuff is trivial. We have to do one key conversion (Eq.1):The first factor on the right is what U.S. EPA standards are defined in. How do we find the second factor? Turns out its reciprocal is something called the F-factor, which is a ratio of flue gas produced per heat generated by a fuel. F-factors are determined by using stoichiometric calculations, explained further on this EPA page.
This conversion assumes that we are using bituminous coal, which has an F-factor of 9780 dscf/mmBtu or 1800 scf CO2/mmBtu. (Here dscf stands for “dry standard cubic feet” and scf stands for “standard cubic feet,” and scf CO2/mmBtu means standard cubic feet of CO2 emitted per mmBtu of coal.)
So, for an example: the US standard for SO2 new coal power plants is 0.15 lb/mmBtu. We divide by the bituminous coal F-factor, 1800 scf CO2/mmBtu to get (lb of SO2/cubic feet of CO2). Then we divide that by 12% because we assume that takes CO2 up 12% of the volume of gas. Then we convert lb to mg (1:4.54E5) and cubic feet to cubic meters (3.28^3:1), and we get about 160 mg/m3, and we’re done.
To summarize, the assumptions made in this conversion:
1) The coal plants use bituminous coal of F-factor 9780 dscf/mmBtu or 1800 scf CO2/mmBtu.
2) Flue gas is 12% CO2.
Another useful unit in emissions standards is ppm, parts per million by volume. I’m not going to lie, I didn’t try to dissect this one to pieces. The conversion looks like this (Eq. 2):
We got the term on the left of Eq. 2 by using Eq. 1. Now we want to convert that number into ppm, so we need the factor on the right. This term is called the K value and it comes from the ideal gas law. To do this we have to convert mass to volume, so we have to assume all sorts of things about pressure and temperature. I’m not going to go into detail on this one because, well, I haven’t had to deal with ppm yet. The K-value for SO2 is 1.66E-7 (pounds of SO2/cubic feet of flue gas/ppm).