Identifying the Median Grade-Tonnage Curve from the Global Database of VMS Copper Mining Projects

Bell, Peter (2026): Identifying the Median Grade-Tonnage Curve from the Global Database of VMS Copper Mining Projects.

Abstract

This paper presents a statistical analysis of the global database of Volcanogenic Massive Sulphide (VMS) mineral deposits. The paper shows the joint and partial probability distributions for copper equivalent grade and total tonnage based on current metals prices for copper, zinc, lead, and gold. The article develops a new method using the joint distribution to identify the set of quantile values for grade and tonnage that have approximately 50% probability; this set of quantile values represents the median grade-tonnage curve for VMS deposits around the world. The article also shows how to analyze individual projects in comparison with the global database. For example, the size of the Shamlugskoe mine in Armenia is ranked according to the global database. For another example, a model of the exploration project called Mount Sicker is presented and compared to nearby projects that are in the global database.

• Item Type: MPRA Paper
• Commentary on: Bell, Peter (2025): Mining Exploration Business Valuation Simulations with Global VMS Deposits Database.
• Language: English
• Keywords: Natural Resources, Mining, Copper, Zinc, Volcanogenic Massive Sulphide, Metals Grade, Deposit Tonnage, Grade-Tonnage Curve, Probability Distribution, Median Path, Statistical Analysis, Simulation, Quantile
• Subjects: A - General Economics and Teaching > A1 - General Economics; A - General Economics and Teaching > A1 - General Economics > A19 - Other; B - History of Economic Thought, Methodology, and Heterodox Approaches > B5 - Current Heterodox Approaches; B - History of Economic Thought, Methodology, and Heterodox Approaches > B5 - Current Heterodox Approaches > B59 - Other; C - Mathematical and Quantitative Methods > C0 - General; C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C14 - Semiparametric and Nonparametric Methods: General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C15 - Statistical Simulation Methods: General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C18 - Methodological Issues: General; C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics; C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C40 - General; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63 - Computational Techniques ; Simulation Modeling; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C69 - Other; C - Mathematical and Quantitative Methods > C8 - Data Collection and Data Estimation Methodology ; Computer Programs; C - Mathematical and Quantitative Methods > C8 - Data Collection and Data Estimation Methodology ; Computer Programs > C81 - Methodology for Collecting, Estimating, and Organizing Microeconomic Data ; Data Access; D - Microeconomics > D2 - Production and Organizations; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D81 - Criteria for Decision-Making under Risk and Uncertainty; G - Financial Economics > G1 - General Financial Markets; G - Financial Economics > G1 - General Financial Markets > G17 - Financial Forecasting and Simulation; G - Financial Economics > G3 - Corporate Finance and Governance; G - Financial Economics > G3 - Corporate Finance and Governance > G31 - Capital Budgeting ; Fixed Investment and Inventory Studies ; Capacity; H - Public Economics > H2 - Taxation, Subsidies, and Revenue; H - Public Economics > H2 - Taxation, Subsidies, and Revenue > H25 - Business Taxes and Subsidies; K - Law and Economics > K2 - Regulation and Business Law; K - Law and Economics > K2 - Regulation and Business Law > K23 - Regulated Industries and Administrative Law; L - Industrial Organization > L2 - Firm Objectives, Organization, and Behavior; L - Industrial Organization > L5 - Regulation and Industrial Policy; L - Industrial Organization > L7 - Industry Studies: Primary Products and Construction; L - Industrial Organization > L7 - Industry Studies: Primary Products and Construction > L72 - Mining, Extraction, and Refining: Other Nonrenewable Resources; Q - Agricultural and Natural Resource Economics ; Environmental and Ecological Economics > Q3 - Nonrenewable Resources and Conservation; Q - Agricultural and Natural Resource Economics ; Environmental and Ecological Economics > Q3 - Nonrenewable Resources and Conservation > Q32 - Exhaustible Resources and Economic Development; Q - Agricultural and Natural Resource Economics ; Environmental and Ecological Economics > Q3 - Nonrenewable Resources and Conservation > Q33 - Resource Booms; Q - Agricultural and Natural Resource Economics ; Environmental and Ecological Economics > Q5 - Environmental Economics; Y - Miscellaneous Categories > Y1 - Data: Tables and Charts

References

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Bell, P. (2018a). "Simulating Mine Revenues with Historical Gold Price Data from the Bank of England," MPRA Paper 89420, University Library of Munich, Germany. https://mpra.ub.uni-muenchen.de/89420/

Bell, P. (2018b). "Valuation Simulation for a Net Smelter Return Royalty on a Mining Project," MPRA Paper 87683, University Library of Munich, Germany. https://mpra.ub.uni-muenchen.de/87683/

Bell, P. (2018c). "Evaluating the Kemess Stream sold by Centerra Gold in 2018," MPRA Paper 87014, University Library of Munich, Germany. https://mpra.ub.uni-muenchen.de/87014/

Bell, P. (2025a). "Mining Exploration Business Valuation Simulations with Global VMS Deposits Database," MPRA Paper 126072, University Library of Munich, Germany. https://mpra.ub.uni-muenchen.de/126072/

Bell, P. (2025b). "Mining Exploration Business Strategy around Logging Roads," MPRA Paper 126635, University Library of Munich, Germany. https://ideas.repec.org/p/pra/mprapa/126635.html

Bell, P. (2025c). "New Methods for Mathematical Optimization of Mine Plans using Theory of Constraints and Activity-Based Costing," MPRA Paper, University Library of Munich, Germany.

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Cowan, E.J. 2014. ‘X-ray Plunge Projection’— Understanding Structural Geology from Grade Data. In AusIMM Monograph 30: Mineral Resource and Ore Reserve Estimation — The AusIMM Guide to Good Practice, second edition, pp. 207–220.

Poniewierski, Julian 2025. "Block Model Knowledge for Mining Engineers - An Introduction", https://www.deswik.com/whitepapers/block-model-knowledge-for-mining-engineers-an-introduction

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