A linear programming and stochastic analysis of mining replacement rate for typical Bushveld Complex platinum reef conventional mining under variable geological losses

摘要

The Merensky and UG2 reefs of the Bushveld Complex in South Africa are currently the largest source of known platinum resources and reserves in the world. Conventional, hybrid and mechanised mining methods are used to extract the platinum reefs. Conventional mining is the most prevalent mining method. In conventional mining, development precedes stoping primarily to provide access to and demarcate the stopes. Mining replacement rate is the rate at which development generates new stopes to replace depleting ones thus, sustaining production. Therefore it is imperative to adopt an appropriate mining replacement rate that carefully balances development and stoping, noting that financial wisdom demands deferring development as far as possible into the future because it is a cost, while operationally, deferring development sacrifices operating flexibility. Inadequate operating flexibility often leads to production shortfalls or working in inadequately prepared stopes often compromising safety. This problem is compounded by geological losses in the form of potholes, dykes and faults whose exact locations, extent and characteristics are never known with certainty prior to mining. Existing operations use mining replacement rates based on empirical approaches. This paper presents a linear programming and stochastic analytical approach to explore mining replacement rate within the range 10% to 60% for geological losses typical of Bushveld Complex platinum reefs. This paper reports work on a current honours research project in the School of Computational and Applied Mathematics at the University of Witwatersrand (Wits), which is being pursued as an off-shoot project from a PhD research study in the Wits School of Mining Engineering and was presented to the 2009 Mathematics in Industry Study Group (MISG) in South Africa.