Incorporation of 3-D Mixing in Long-term ‎Production Scheduling Optimization for Block ‎Caving Mines

  • Author / Creator
    Khodayari, Firouz
  • As open-pit mines go deeper, because of the massive amount of waste removal which is ‎required to ‎extract the ore as well as high operational costs per tonne, underground mining has ‎become more ‎attractive. Block caving is the only underground mining method that its production ‎rates and ‎operating costs are comparable to open-pit mining. Therefore, block-cave mining has ‎become ‎more popular in the last few years, and the trend is ‎expected to continue.‎‏ ‏Long periods ‎of ‎development and the resulting high capital cost is one of the main challenges of this ‎method; ‎therefore, a practical production schedule with the possibility of generating higher ‎revenues ‎earlier in the project can significantly improve the cash flow by increasing the net ‎present value of ‎the project and change a deep low-grade ore resource to a valuable ore reserve. ‎In block caving, ‎production scheduling is the decision of the amount of caved rock to ‎extract ‎from drawpoints ‎in ‎different periods. Relying only on manual planning methods or computer ‎software based on ‎heuristic algorithms will lead us to mine schedules that are not necessarily the ‎optimal global ‎solution. Instead, the mathematical programming can guarantee the optimality, or ‎give us an ‎estimation of how close the answer is to the optimal solution in case of integer ‎programming.‎ This study presents a stochastic optimization model that aims to maximize the net ‎present ‎value of block caving operations. Technical constraints such as mining capacity, ‎production ‎grade, number of active drawpoints, continuous mining during the life of the mine, ‎mine reserve, ‎draw rate, draw life, precedence of extraction among slices, and mining direction ‎are included in ‎the model. One of the main differences between ‎block caving and other mining ‎methods is ‎the ‎influence of the material flow on ‎production and draw control in general. ‎Some ‎production ‎scheduling optimization models for block caving exist in the literature; however, few ‎of them ‎consider the material flow and resulting dilution within the production schedule. ‎ In this research, to achieve more reliable production schedules, a 3-D mixing methodology ‎is ‎proposed to be incorporated in the production scheduling optimization model; a model ‎that ‎maximizes the net present value of the mining project while taking different scenarios of ‎mixing ‎into consideration. The scenarios are generated based on the particles that fall into a cone ‎of ‎movement, CoM, to capture horizontal and vertical mixing. The mathematical ‎programming ‎formulation is a stochastic mixed integer linear programming model where decision ‎variables are ‎associated with individual slices and draw columns, the ‎output production ‎schedule ‎determines which slices are extracted from each ‎drawpoint in each period. The objective ‎function ‎maximizes the net present value of the project during the ‎life of the mine ‎and ‎minimizes ‎deviations of production grades and tonnages from the defined ‎targets for ‎all ‎probable scenarios ‎resulting from the movements of the fragmented rock ‎between ‎drawpoints. ‎This feature provides ‎a flexible tool for mine planners to ‎control the draw based on the ‎company’s goals during ‎the life ‎of the mine.‎ The model was tested on different real-case block caving mines in different steps ‎of ‎development. The last version of the model is a block caving scheduling optimizer, BCSO, ‎which ‎includes mixing in the production scheduling optimization. The BCSO was verified on a ‎block ‎caving mine with 424 drawpoints; also, a number of production schedules were generated ‎for the ‎same mine using GEOVIA PCBC software. Based on the features of the BCSO and ‎PCBC, ‎three different cases were tested: without draw rate constraint and mixing, with draw ‎rate ‎constraint and without mixing, and with draw rate constraint and mixing. In each case, ‎the ‎BCSO was validated against three different scheduling methods that exist in PCBC: ‎AUTO, ‎SMOOTH, and COMBO. The resulting production schedules show that the BCSO can ‎improve ‎the NPV of the project by 2% ‎to 4% compared to the best case generated by PCBC. In ‎all cases, ‎the precedence among drawpoints, which is traditionally decided manually, was ‎determined by ‎the mining direction finder embedded in BCSO and used for PCBC as well. ‎Application of this ‎feature of BCSO into production scheduling improves the profitability of ‎block caving mines. Due to ‎the limitations of PCBC, not all of the constraints that BCSO is ‎capable to model were used for ‎the comparison purposes. However, an additional case was run ‎by BCSO to test the target grade ‎option and it was shown that the desired target grade of 1% ‎copper can be achieved for all ‎periods during the life of the mine when the processing plant ‎operates only by a certain grade. In ‎addition, other constraints such as draw life and number of ‎active drawpoints can be ‎implemented in the BCSO based on the technical and economic ‎limitations of the ‎mine. ‎ The major novelties of this thesis are: determination of the best mining direction in the block ‎caving layout and defining precedence of drawpoints accordingly, NPV maximization for block ‎caving mines using mathematical programming where technical constraints of the operations are ‎satisfied, minimization of deviations of production tonnages and grades from the company’s ‎targets, and incorporation of caving flow and its uncertainties in the production scheduling ‎optimization model.

  • Subjects / Keywords
  • Graduation date
    Fall 2018
  • Type of Item
  • Degree
    Doctor of Philosophy
  • DOI
  • License
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