• industrial ecology;
  • Markov chains;
  • metal cycles;
  • resource efficiency;
  • scrap recycling;
  • technological lifetime


Markov chain (MC) modeling is a versatile tool in policy analysis and has been applied in several forms to analyze resource flows. This article builds on previous discussions of the relationship among absorbing Markov chains (AMCs), material flow analysis (MFA), and input-output (IO) analysis, and presents a full-scale application of MC modeling for a particular globally relevant, nonrenewable resource, namely nickel. The MC model presented here is built on comprehensive, recently compiled nickel flow data for 52 geographic regions. Considering all possible cycles of recycling and reuse, nickel extracted in 2005 is estimated to have a technological lifetime of 73 ± 7 years. During its global journey, nickel enters use, for some application somewhere in the world, an average of three times, the largest share of which occurs in China. Nickel entering fabrication in 2005 is estimated to enter use approximately four times. Over time, nickel is lost to the environment and as a tramp element in carbon steel; the final distribution of nickel among these absorbing states is 78% and 22%, respectively. Of all the nickel in ore extracted in 2005, fully 28% will eventually end up in the tailings, slag, and landfills of China. MC results are also combined with geographically specific life cycle inventory data to determine the overall energy invested in nickel during its many cycles of use. MCs provide a powerful tool for tracking resources through the network of global production, use, and waste management, and opportunities for further integration with other modeling efforts are also discussed.