Methane is generated via the anaerobic decomposition (biological degradation in the absence of oxygen) of solid waste in landfills. Collecting the methane for use as a fuel rather than allowing it to disperse into the atmosphere provides a useful supplement to natural gas as an energy source.

If a batch of waste with mass M (tonnes) is deposited in a landfill at t = 0, the rate of methane generation at time t is given by

where V̇_CH4 is the rate at which methane is generated in standard cubic meters per year, k is a rate constant, L₀ is the total potential yield of landfill gas in standard cubic meters per tonne of waste, and Mwaste is the tonnes of waste in the landfill at t = 0.

(a) Starting with Equation 1, derive an expression for the mass generation rate of methane, Ṁ_CH4(t).

Without doing any calculations, sketch the shape of a plot of Ṁ_CH4 versus t from t = 0 to t = 3 y, and graphically show on the plot the total masses of methane generated in Years 1, 2, and 3. Then derive an expression for M_CH4 (t), the total mass of methane (tonnes) generated from t = 0 to a time t.

(b) A new landfill has a yield potential L₀ = 100 SCM CH₄/tonne waste and a rate constant k = 0:04 y^-1. At the beginning of the first year, 48,000 tonnes of waste are deposited in the landfill. Calculate the tonnes of methane generated from this deposit over a three-year period.

(c) A colleague solving the problem of Part (b) calculates the methane produced in three years from the 4:8 × 10⁴ tonnes of waste as

where Ṁ_CH4 is the first expression derived in Part (a). Briefly state what has been assumed about the rate of methane generation. Calculate the value determined with this method and the percentage error in the calculation. Show graphically what the calculated value corresponds to on another sketch of Ṁ_CH4 versus t.

(d) The following amounts of waste are deposited in the landfill on January 1 in each of three consecutive years.

	Waste (tonnes)
Year 1	48,000
Year 2	45,000
Year 3	54,000

Calculate the metric tons of CH4 generated through the end of the third year.

Exploratory Exercises—Research and Discover

(e) Explain in your own words the benefits of reducing the release of methane from landfills and of using the methane as a fuel instead of natural gas.

(f) One way to avoid the environmental hazard of methane generation is to incinerate the waste before it has a chance to decompose. What problems might this alternative process introduce?

Transcribed Image Text:

VCH, (4) = KL,M wastee-t (1)