Methane, a powerful greenhouse gas, is generated viathe anaerobic decomposition of solid waste in landfills. Collectingthe methane for use as a gaseous fuel rather than allowing it to bereleased to the atmosphere provides an alternative to natural gasas an energy source and has a beneficial effect on the environment.If a batch of waste with mass M(tonnes) [1 tonne or 1 metric ton =1000 kg] is deposited in a landfill at t=0, the rate of generationof methane at a later time t is given by the following equation VCH4 (t) = kL o M waste e -kt where: V CH4 (SCM CH 4 /y) = methanegeneration rate [SCM = m 3 (STP)] K = rate constant (y -1 ), ameasure of how fast the waste decomposes L o = landfill gas yieldpotential [SCM CH 4 /tonne waste] M waste = tonnes of wastedeposited at t= 0
a. Explain in your own words the benefits of reducing the releaseof methane from landfills and using the methane as a fuel insteadof natural gas.
b. Starting with the above equation, derive an expression for themass generation rate of M CH4 (t)[tonnes CH 4 /y]. Without doingany calculations, sketch the shape of a plot of M CH4 vs t from t=0to t = 3y, and graphically show on the plot the total masses ofmethane generated in YEARS 1, 2, and 3 (Hint: Remember yourcalculus.) Then derive an expression for M CH4 (t)(tonnes CH 4 ),the total methane generated from t =0 to an arbitrary time t.
c. A new landfill has a yield potential L o = 100 SCM CH 4 /tonnewaste and a rate constant k = 0.04y -1 . At the beginning of itsfirst year, 48,000 tonnes of waste are deposited. Calculate thetonnes of methane generated from this deposit over a three-yearperiod.
d. A junior engineer solving the problem of Part c calculates themethane produced in three years from the 48,000 waste deposit as MCH4 (t=3) = M CH4 (t=0){tonnes CH 4 /y}x 1y + M CH4 (t=1)x1 + M CH4(t=2)x1 where M CH4 is given by the first expression derived inPart b.
-- -- -- Briefly state what the engineer is assuming about the rateof methane generation
-- -- -- - Calculate the value she would determine and thepercentage error in her calculation, and show graphically what thecalculated value corresponds to on another sketch of M CH4 vst.
-- -- - The answer to Part c is 390 tonnes CH 4 . When one of thetext authors first did the calculation of M, the result was 210tonnes CH 4 . The author immediately knew that something had to bewrong in the calculation. Explain her reasoning.
e. The following amounts of waste are deposited in the landfill onJanuary 1 in each of three consecutive years: Waste (tonnes) Year 148,000 Year 2 45,000 Year 3 54,000 Calculate the metric tons ofmethane generated through December 31 of the third year.
f. One way to avoid the environmental hazard of methane generationis to incinerate the waste before it has a chance to decompose.What problems might this alternative process introduce?