MATHEMATICAL MODELLING AND OPTIMIZATION OF ORE EXTRACTION PROCESSES IN MINING ENGINEERING

Abstract

In this study we show a mathematical model in mining systems for the processes of ore extraction in relation to mining industries in Papua New Guinea. Major mining operations such as Ok Tedi Mine, Porgera Gold Mine and Newmont Lihir Gold Mine have over decades produced sustainable quantities of gold and copper with contributing more than 70% of Papua New Guinea’s export earnings in the recent years (Githiria, 2019). Regardless of this importance in economy, mining operations are affected frequently by variables such as equipment efficiency, reserve quantity, extraction rate and stochastic randomness that are a result of geological uncertainties are all integrated in the model. To optimize and predict the rate of ore extraction under geological and operational constraints we aim to develop a framework.

We formulate a system of differential equations to represent the depletion of ore over time (Øksendal, 2003) (Ross, 2014) and an additional stochastic component is then introduced to cater for random events in mining operations (Øksendal, 2003). Numerical simulations are conducted using Excel, to analyze system behavior under different extraction strategies, using an initial ore reserve of 1000 units with k=0.3, be the extraction coefficient. The deterministic model showed that from 1000 units the ore reserve went down exponentially to roughly 50 units after a span of 10 years. Whereas a fluctuating pattern was produced by the stochastic model with non-uniform ore quantities between 120 and 820 units which is due to the effect of uncertainty. By comparing aggressive, balanced and slow extraction strategies, the optimization simulation shows that the highest cumulative profit of K7710.00 was generated while extending the mine lifespan by more than 40% through the balanced extraction policy compared to the aggressive and slow extraction policy.

Findings indicate that optimal and well-designed extraction policies can improve recourse usage substantially while at the same time minimize operational cost (MacNeil & Dimitrakopoulos, 2017). The model illustrates that uncontrolled extraction leads to rapid depletion, on the contrary, sustainability is enhanced through controlled strategies.

This study enhances the role of applied mathematics in mining engineering by presenting a quantitative framework for making of decisions in ore extraction. The model can be calibrated using real data in mining to improve planning and operational efficiency in Papua New Guinea.