Some arithmetic

I read about a program to convert marine waste—fishing nets and other gear—into energy. The claim is made that 1 ton of waste can power a household for 5 months. That number sounds high, but not completely unrealistic. Does it add up?

Well, a Department of Energy survey measures the typical American household’s consumption of electricity in 1993 at 9,965 kilowatt-hours per year, of which about half goes into heating and cooling, water heaters, and refrigerators, and the other half into other appliances. So 9,965/12 = 830 kWh per month.

Myself, I am somewhat more profligate, and I bought 16,290 kWh from Dominion Virginia Power for my all-electric home in 2008. Ah, but we read that mixed-fuel homes use less electricity than all-electric homes (as you would certainly expect); the average all-electric home burned 15,639 kWh/year in 1993.

At any rate, let’s use the 830 kWh/month figure, just to pick a number.

Now, how much energy can be extracted from something by burning it? Household waste has an energy density of 8 to 11 megajoules per kilogram. Bituminous coal, for comparison, comes in at 24 MJ/kg, wood at 6 to 17 MJ/kg, and gasoline at 46.4 MJ/kg. Plastics score in the coal-gasoline range. Let’s use 15 MJ/kg. Now for some conversions (with lots of roundoff):

1 ton of waste = 907 kilograms of waste
907 kg · 15 MJ/kg = 13,605 megajoules of energy
1 kWh = 3.6 · 106 joules, so
13,605 MJ · 1 kWh / 3.6 MJ = 3,780 kilowatt-hours per ton of waste

And our typical household will go through 830 kWh/month · 5 months = 4,150 kWh. So we’re in the ballpark, assuming the combustion of the waste is fairly efficient.

Makes me remember the can in the back yard of my grandparents’ house where we would burn the trash. How many watt-hours did we let escape?