Parametric analysis in surface-mine reserve definition: the inherent error and its correction

Lemieux, M.
Organization: Society for Mining, Metallurgy & Exploration
Pages: 8
Publication Date: Jan 1, 2000
Introduction The objective of the design and operation of a mine is to make as much money as possible within certain reasonable and responsible constraints. The imposition of constraints on the objective of maximizing profits can result in an optimum mine design. This paper deals with the maximization of profits. Optimization will be discussed in a future paper. In the mining industry, it is generally accepted that the maximum economic recovery is defined by identifying the reserves and the sequence of mining that results in maximum net present value (NPV) or discounted cash flow-rate of return (DCF-ROR), as indicated in Fig. 1 (see Lemieux, 2000). Current parametric analyses techniques, such as varying the mining costs; profit reservation; sales price or metal content, to define pit limits and mining sequence technically referred to single, double or triple parameterization, do not assure that the curve in Fig. 1 will be maximized. In defining the sequence, the first material to be mined should be the first grouping of recoverable mineral that has the highest after-tax unit value and that forms a feasible mining unit. The assumed mining of the first pit should be followed by the assumed mining of the second most profitable and practical pit or pit expansion. If this process of grouping and sequencing is followed until the profitability approaches zero, the general sequence required to extract the maximum economically recoverable reserve is identified. The curve in Fig. I is constructed by calculating the NPV for a series of sequences, each assuming operations are terminated on successively lower profit pits. If the operation ceases on a pit with too high of a profit, opportunity is lost, and the NPV is lower than the maximum. The NPV curve peaks and then starts to decline before the zero-profit pit is assumed mined. This occurs because the money invested in advanced stripping would have produced a greater return if it was invested at the dis¬count rate. The maximum economically recoverable reserve is defined by the pit limit corresponding to the maximum NPV or DCF-ROR. Pit and phase definition The real challenge of reserve definition is identifying the phasing and after-tax profit per ton, so that the curve in Fig. 1 can be plotted. The after-tax profit cannot be properly addressed until after the pits are designed, the production is scheduled and the cash flow is estimated. Throughout the years, many investigators have ad¬dressed this problem. A major thrust of the famous paper in which Lerchs and Grossman (1965) presented their algorithm was to identify a sequence that would produce a result similar to that identified in Fig. 1. Whittle's (1988) four-dimensional analysis is designed to address this issue. The author addressed this same issue in a paper presented to the 1968 Canadian Institute of Mining national convention (Lemieux, 1968). Without a relatively simple methodology to con¬struct the curve in Fig. 1, the number of iterations in a trial-and-error method becomes prohibitively burden-some. The pit designer seeks a simple pit-planning parameter that will serve as a proxy for the after-tax profit per ton used in defining the curve in Fig. 1. The designer's goal is to apply this pit-planning parameter using standard pit-wall location techniques to design a series of pits that will provide a guide to the sequencing. Common techniques used to position pit walls are strip-ratio limits, highwall incremental analysis, floating-cone methods or "maximizer" applications1. Costs, revenues, noncash charges, taxes and profits are usually structured on a unit basis for use in the pit-wall location analysis. Application of the proxy parameter using the pit-design tools should, ideally, result in the definition of pits and sequences that will maximize the curve in Fig. 1. 1 The pit-design tool frequently referred to in the literature as an "optimizer" defines a pit boundary that maximizes the value contained within based on the input parameters and the safe pit-wall angle. The optimization of the pit design involves selection of rate of production, cutoff grade, product quality and other considerations. These considerations constrain the maximization of value. Therefore, pit-design tools that maximize value should be called "maximizers."
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