Fossil and Nuclear Energy Resources

Coal-bed methane environmental impacts

Coal-bed methane (CBM) is natural gas, mainly methane, that is held by adsorption on the internal surfaces of coal seams. To release it, producers lower the reservoir pressure by pumping water out of the seam, which allows the gas to desorb and flow to the well. The water brought up with the gas, called produced water, often contains dissolved salts, heavy metals and other contaminants picked up from the coal formation. Its disposal, storage in surface ponds, or leakage into aquifers can contaminate surface water and groundwater, and this water contamination is the principal environmental concern of CBM production. By contrast, carbon dioxide emission, nitrogen oxides and sulphur oxides are associated with the combustion of any fuel, not specifically with the extraction of methane from coal seams. Students should therefore link CBM with produced-water management and aquifer protection, and link NOx and SOx with high-temperature combustion and sulphur-bearing fuels.

Radioactive decay of isotopes

Radioactive decay is a first-order random process in which the number of undecayed nuclei N falls exponentially with time, N(t) = N_0 e^{-\lambda t}, where \lambda is the decay constant (unit: year^{-1} if time is in years). The activity is A = \lambda N, and the mean life is \tau = 1/\lambda. The half-life T_{1/2} = \ln 2/\lambda is the time for half of the sample to decay, and it is a common source of error to confuse it with the time for a different fraction to remain. The time needed for the sample to fall to a fraction f of its initial value is t = \ln(1/f)/\lambda. For a remaining fraction of 0.25, t = \ln 4/\lambda = 2T_{1/2}, because two successive halvings give one quarter. This time depends only on \lambda and not on the initial number of atoms N_0, since N_0 cancels in the ratio N/N_0. For example, with \lambda = 0.001 year^{-1}, T_{1/2} \approx 693 years and the time to reach 25 % is \ln 4/0.001 \approx 1386 years, which is about twice the half-life.