Abstract
Production of major minerals and co(by)-product minerals is highly connected. For example, almost 95% of indium production can be derived from zinc mining and processing. In this paper, a Copula–Hubbert model for co(by)-product minerals is proposed and applied for predicting zinc and indium production in the world. Unlike the Hubbert model, a copula function to joint multiple logistic distributions in the Copula–Hubbert model makes the minerals’ production more accurate. Because of geological and mining information asymmetric relationships among mineral deposits, the model is more appropriate to by-product minerals. The empirical result shows that the peak of zinc may arrive in 2030 nearly; however, the peak of indium may reach after 2050. In the future, the peak value and peak date of indium can be affected by the development and utilization efficiency of zinc mining and processing. Finally, some directions on this model are introduced.
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References
Ali, S. H., Giurco, D., Arndt, N., Nickless, E., Brown, G., Demetriades, A., et al. (2017). Mineral supply for sustainable development requires resource governance. Nature, 543(7645), 367–372.
Al-Jarri, A. S., & Startzman, R. A. (1997). Worldwide petroleum-liquid supply and demand. Journal of Petroleum Technology, 49(12), 1329.
Al-Jarri, A. S., & Startzman, R. A. (1999). US oil production and energy consumption–A Hubbert modeling approach to forecast long-term trends in various components of US energy consumption with an emphasis on domestic oil production. Advances in the Economics of Energy and Resources, 11–1999(11), 37–58.
Berg, P., & Korte, S. (2008). Higher-order Hubbert models for world oil production. Petroleum Science and Technology, 26(2), 217–230.
Calvo, G., Valero, A., & Valero, A. (2017). Assessing maximum production peak and resource availability of non-fuel mineral resources: Analyzing the influence of extractable global resources. Resources, Conservation and Recycling, 125, 208–217.
Cavallo, A. J. (2004). Hubbert’s petroleum production model: An evaluation and implications for world oil production forecasts. Natural Resources Research, 13(4), 211–221.
Cherubini, U., Luciano, E., & Vecchiato, W. (2004). Copula methods in finance. New York: Wiley.
Council, N. R. (2008). Minerals, critical minerals, and the US economy. Washington, DC: National Academies Press.
Fang, J. C., Lau, C. K. M., Lu, Z., & Wu, W. S. (2018). Estimating peak uranium production in China - Based on a Stella model. Energy Policy, 120, 250–258.
Feng, L. Y., Li, J. C., & Pang, X. Q. (2008). China’s oil reserve forecast and analysis based on peak oil models. Energy Policy, 36(11), 4149–4153.
Gumbel, E. J. (1961). Bivariate logistic distributions. Journal of the American Statistical Association, 56(294), 335–349.
Harris, T. M., Devkotab, J. P., Khanna, V., Eranki, P. L., & Landis, A. E. (2018). Logistic growth curve modeling of US energy production and consumption. Renewable and Sustainable Energy Reviews, 96, 46–57.
Hayes, S. M., & McCullough, E. A. (2018). Critical minerals: A review of elemental trends in comprehensive criticality studies. Resources Policy, 59, 192–199.
Hubbert, M. K. (1956). Nuclear energy and the fossil fuels/shell development company. Exploration and Production Research Division, Publication, 95, 40.
Jones, T. H., & Willms, N. B. (2018). A critique of Hubbert’s model for peak oil. Facets, 3, 260–274.
Jordan, B. (2018). Economics literature on joint production of minerals: A survey. Resources Policy, 55, 20–28.
Malik, H. J., & Abraham, B. (1973). Multivariate logistic distributions. The Annals of Statistics, 1(3), 588–590.
May, D., Prior, T., Cordell, D., & Giurco, D. (2012). Peak minerals: theoretical foundations and practical application. Natural Resources Research, 21(1), 43–60.
Michaelides, E. E. (2017). A new model for the lifetime of fossil fuel resources. Natural Resources Research, 26(2), 161–175.
Mohr, S. H., & Evans, G. M. (2008). Peak oil: testing Hubbert’s curve via theoretical modeling. Natural Resources Research, 17(1), 1–11.
Mudd, G. M., Jowitt, S. M., & Werner, T. T. (2017a). The world’s by-product and critical metal resources part I: uncertainties, current reporting practices, implications and grounds for optimism. Ore Geology Reviews, 86, 924–938.
Mudd, G. M., Jowitt, S. M., & Werner, T. T. (2017b). The world’s lead-zinc mineral resources: Scarcity, data, issues and opportunities. Ore Geology Reviews, 80, 1160–1190. https://doi.org/10.1016/j.oregeorev.2016.08.010.
Nassar, N. T., Graedel, T. E., & Harper, E. (2015). By-product metals are technologically essential but have problematic supply. Science Advances, 1(3), e1400180.
Pesaran, M. H., & Samiei, H. (1995). Forecasting ultimate resource recovery. International Journal of Forecasting, 11(4), 543–555.
Suh, S., Bergesen, J., Gibon, T., Hertwich, E., & Taptich, M. (2017). Green technology choices: The environmental and resource implications of low-carbon technologies. United Nations Environment Programme: Nairobi, Kenya.
Szklo, A., Machado, G., & Schaeffer, R. (2007). Future oil production in Brazil - Estimates based on a Hubbert model. Energy Policy, 35(4), 2360–2367.
Tilton, J. E. (2018). The Hubbert peak model and assessing the threat of mineral depletion. Resources, Conservation and Recycling, 139, 280–286.
Valero, A., & Valero, A. (2010). Physical geonomics: Combining the exergy and Hubbert peak analysis for predicting mineral resources depletion. Resources, Conservation and Recycling, 54(12), 1074–1083.
Valero, A., Valero, A., Calvo, G., & Ortego, A. (2018). Material bottlenecks in the future development of green technologies. Renewable and Sustainable Energy Reviews, 93, 178–200.
Valero, A., Valero, A., & Torres, C. (2009). Exergy and the Hubbert Peak. Assessment of the Scarcity of Minerals on Earth. In IMECE 2008: Proceedings of the ASME international mechanical engineering congress and exposition–2008 (Vol 8, pp. 507–516).
Wang, J. Z., Jiang, H. Y., Zhou, Q. P., Wu, J., & Qin, S. S. (2016). China’s natural gas production and consumption analysis based on the multicycle Hubbert model and rolling Grey model. Renewable and Sustainable Energy Reviews, 53, 1149–1167.
Wellmer, F. W., & Scholz, R. W. (2017). Peak minerals: What can we learn from the history of mineral economics and the cases of gold and phosphorus? Mineral Economics, 30(2), 73–93.
Werner, T., Mudd, G. M., & Jowitt, S. M. (2017a). The world’s by-product and critical metal resources part III: A global assessment of indium. Ore Geology Reviews, 86, 939–956.
Werner, T. T., Mudd, G. M., & Jowitt, S. M. (2017b). The world’s by-product and critical metal resources part II: A method for quantifying the resources of rarely reported metals. Ore Geology Reviews, 80, 658–675.
Acknowledgments
This research was funded by the National Natural Science Foundation of China (Nos. 71991482, No. 41572315), the Fundamental Research Funds for National Universities of China University of Geosciences (Wuhan) (No. 2201710264), Humanities and Social Sciences Fund of the Ministry of Education (No. 19YJCZH168) and the scholarship from the China Scholarship Council (CSC) (No. 201906410038). We thank for the professional language services by Mr. Humayoun Akram, Dr. Saleem Ali and Writing Center in University of Delaware. Finally, we also thank the editor’s and reviewers’ suggestions and comments.
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Xu, D., Zhu, Y. A Copula–Hubbert Model for Co(By)-Product Minerals. Nat Resour Res 29, 3069–3078 (2020). https://doi.org/10.1007/s11053-020-09643-1
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DOI: https://doi.org/10.1007/s11053-020-09643-1