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Biogas fueled electricity plant
How much biogas could a sewage treatment plant produce from a population of 100,000 people through a well-planned sewer system?
Here is a quick back of the envelope calculation to get this page started. Please find sources or corrections for these assumptions.
- personal effluent = 120 liters/(person*day)
- Effluent dirtyness = 800 mgBOD/l
- biogas coefficient = 0.395 lbiogas/gBOD 
- digestor efficiency = 0.85
- energy density of biogas = 0.036 MJ/l 
- Volume = 100,000 people * 120 liters/(person*day) * 800 mgBOD/l * 1 g/1000 mg * 0.395 lbiogas/gBOD * 0.85 = 3,223,200 liters/day of biogas 
- Energy = 3,223,000 l/day * .036 MJ/l = 116,000 MJ/day (or about 32,232 kWh/day)
- Energy/person = 116,000 MJ/day / 100,000 people = 1.16 MJ/person/day (or about 0.32 kWh/person/day)
By comparison, in 2008, the per capita primary energy consumption of the United States was 87,216 kWh/yr or 239 kWh/day. Thus in a developed country such as the US, the energy recoverable from a person's bodily wastes can only provide a tiny fraction of his or her primary energy consumption.
By another comparison, in 2009, the average annual electricity use for a U.S. home was about 11.7 kWh/person/day.  So biogas could meet 0.32 kWh / 11.7 kWh = 2.7% of our daily electricity usage.
Comparison with food intake
The energy content of human waste cannot exceed the energy content of the food that humans eat (energy in equals energy out plus accumulation). If the average person eats 2,500 food calories per day, that is equal to:
If a biogas plant produces 61,000 kWh/day from the waste of 100,000 people, that represents about 61,000 kWh / 290,750 kWh = 21% of the energy content of the food they eat. Thus the 61,000 kWh figure satisfies the sanity check of being less than the energy content of the food eaten by the people producing the sewage. The actual energy content of human waste varies with diet. For example, diets higher in fiber produce larger stool volume, i.e. the human digestive tract recovers less of the energy content of the food and more of it ends up in feces.
- 1 gram COD = 395 mL methane @ 35°C, 1 atm from http://fyi.uwex.edu/midwestmanure/files/2013/03/Myths-Minsconceptions-of-Digesters-Zitomer.pdf
- According to http://www.ncbi.nlm.nih.gov/pubmed/24185054, an improved biogas system can produce 12.5 m^3 per population equivalent per year. That is equivalent to 34.2 l/day/person which is close to our calculations.
- "In 2009, the average annual electricity consumption for a U.S. residential utility customer was 10,896 kWh, an average of 908 kilowatthours (kWh) per month" from http://www.eia.gov/tools/faqs/faq.cfm?id=97&t=3 and average household size in 2000 was 2.59 people from http://factfinder.census.gov/servlet/SAFFFacts. So 908 kWh / 2.59 people / 30 day/month = 11.7 kWh/person/day.