Markov chain modeling of the global technological lifetime of copper

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