In the last post we looked at the basic composition of landfill gas. Now let’s use that information to calculate the density. The density of a gas is a critical factor when measuring its flow rate. Density is mass divided by volume, so let’s first calculate the volume of a quantity of landfill gas.
As you may remember from high school chemistry, the properties of a gas change dramatically with temperature and pressure, as described by the ideal gas law (P is the gas pressure, V is the volume, n is the number of moles of the gas, R is a constant called the Universal Gas Constant, and T is temperature):
So where do we start? Well, we can easily search online and find that R has a value of 8.314 J/(mole*K) and we can calculate everything assuming we are working with 1 mole of gas. Because that leaves three real variables (pressure, volume and temperature), we’ll need to fix two and solve for the third. This requires some additional information about landfill gas extraction systems.
After talking with a bunch of landfills, I’ve found that the system pressure in the gas extraction system is typically around 40-50” of water (vacuum, measured relative to the atmospheric pressure). 40” of water is equivalent to 99.6 millibar, so for simplicity I’ll assume the landfill gas is at 900 mbar (since 40” of vacuum means -99.6 mbar relative to the atmosphere, which is usually around 1 bar). In SI units, this is 90,000 Pascal.
Because landfill gas is a byproduct of anaerobic digestion, it is usually around 40° C, or 313.15 K (in SI units). Now that I’ve specified a value for P and T, I can calculate the volume of 1 mole of hypothetical gas:
There are tons of good online calculators to do basic calculations with the ideal gas law, like this one. In the next post, we’ll combine this result with the information we found last time about landfill gas compositions in order to calculate some density ranges.