Waste Decomposition Calculator

This model treats decomposition as first-order decay: the mass loss rate is proportional to the mass still present, giving M(t) equal to M0 times e raised to minus k times t. The rate constant k has units of reciprocal years and encodes how biologically accessible the substrate is. Readily hydrolysable material such as food scraps and garden waste carries k values around 0.1 to 0.4 per year; paper and cardboard fall near 0.04 to 0.06; wood and textiles run 0.02 to 0.03; and lignin-rich or synthetic material sits below 0.01. Because the decay is exponential, the derived timescales are fixed multiples of one another: half-life is ln(2)/k, 90 percent loss takes ln(10)/k, and 99 percent takes ln(100)/k, which is always about twice the 90 percent time. Temperature is handled through a Q10 factor of 2, meaning the rate doubles for every 10 degrees C rise from the 25 degrees C reference. That approximation holds reasonably from roughly 5 to 45 degrees C; below about 5 degrees microbial activity nearly stops, and above about 65 to 70 degrees the responsible organisms die off, so the model over-predicts at both extremes. Two further limitations matter. First-order decay assumes a single homogeneous substrate, whereas real refuse is a mixture whose easy fraction disappears first, leaving an apparently slowing residue. Second, the methane estimate here is deliberately simple, assuming decomposed organic mass yields biogas at roughly 50 percent methane by volume, methane density 0.717 kg per cubic metre, and a 100-year global warming potential of 28. Field landfills also lose gas to oxidation in cover soil and to collection systems, which this does not deduct.

First-order decay was borrowed into waste science from radiochemistry, where Ernest Rutherford and Frederick Soddy formulated the exponential decay law and the half-life concept in 1902. Ecologists adopted the same mathematics for litter breakdown decades later; Jerry Olson's 1963 paper in the journal Ecology on energy storage and decomposition in ecological systems established the single-exponential litter decay constant, still written as k, as the standard descriptor of organic matter turnover. The temperature adjustment traces to Jacobus van't Hoff's late nineteenth-century work on reaction rate and temperature, later simplified by biologists into the Q10 rule of approximate doubling per 10 degrees C. Application to buried municipal refuse followed the discovery that landfills are large methane sources. US landfill gas recovery projects began in the early 1970s, and the EPA established the Landfill Methane Outreach Program in 1994. The regulatory model most commonly used, LandGEM, packages exactly this first-order decay structure with default k values for arid and wet climates. The Intergovernmental Panel on Climate Change adopted a first-order decay method for solid waste disposal sites in its 1996 revised guidelines and formalized it in Volume 5 of the 2006 National Greenhouse Gas Inventories Guidelines, which introduced the degradable organic carbon fraction, the methane correction factor for site management, and waste-type-specific k values that countries still use for national reporting.