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Incorporation of 3-D Mixing in Long-term Production Scheduling Optimization for Block Caving Mines
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- Author / Creator
- Khodayari, Firouz
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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. -
- Graduation date
- Fall 2018
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- Type of Item
- Thesis
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- Degree
- Doctor of Philosophy
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- License
- Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.