Markov chain modeling of the global technological lifetime of copper

摘要: Abstract Markov chain modeling is applied to the global anthropogenic copper cycle for year 2000. The lifetime of varies from product and region region, as well through time. Assumptions average lifetimes are therefore subject a high degree uncertainty. A large state transition table created that encompasses life-cycle stages (mining, smelting, refining, fabrication, use, waste management, scrap, final disposal), five end-uses (buildings, transportation, consumer products, electrical equipment, machinery) in eight world regions, including trade at every stage. system requires closure by mass balance, so all possible routes recycling considered. Transitions between each pair states calculated using previous material flow analysis data. main result an atom used 1.9 times human society before it enters disposal. Scaling stage gives total technological 60 years. sensitivity model order test robustness results. Several scenarios also considered: increasing rate 70%, applying European or North American in-use share cathode scrap markets taken Asia 50%. limitations approach discussed, further research opportunities affords.