The generation of a mine sequence for a block caving mine is challenging given it represents the direction for opening draw points. Several complex theories and mathematical optimizations have been presented in the last decade, however most of them are too complex to provide a solution for real-life block caving mines when the dimension exceeds the capacity of these models, or super computers are used and processing time is an issue. In this new series we will present a new option for optimizing mine sequences using the concept of ‘best and worst case’ adopted from open pit mines. 

By @DV - Principal Consultant Caving Business Unit Dassault Systèmes, GEOVIA

INTRODUCTION

The choice of initiation point for the sequence and the preferred direction can be influenced by several factors including shape of the orebody, access infrastructure, grade distribution, in situ stress directions and magnitudes, for example, however one of the main objectives is to optimize the value of a project by creating a production schedule that maximizes the Net Present Value (NPV).

There have been many studies and theories developed attempting to solve this problem, utilizing very complex mathematical approaches where the number of variables, constraints and formulations result in a solution that is difficult to implement and not flexible enough to add new constraints, such as mixed integer linear programming (Y. Pourrahimian, H. Askari-Nasab, D. Tannant, 2012) or integer programming (T. Elkington, L. Bates, O. Richter, 2012).

This paper will discuss an option to generate an optimal mine sequence using the approach of ‘best and worst case’ intensively used in open pit optimization (Smith, 2001) applied in Footprint Finder.

FOOTPRINT FINDER

Footprint Finder, a module of GEOVIA PCBC™, was developed primarily to support a quick study of a block model to find the best elevation and orientation for locating an extraction level for block cave mining. Now it supports the creation of a simple production schedule using the sequence as input and offers opportunity to perform several runs in a short period of time to evaluate different options for direction and shape of the cave front for an optimal mine sequence. Some of the characteristic of Footprint Finder include:

• Compare economic values for different footprints within different areas.
• Enable quick changing and evaluation of an economic model.
• Enable a comparison using different amounts of vertical mixing applied to each column using an algorithm based on Laubscher’s mixing method (Laubscher, 1994).

• Enable the construction of block models representing cumulative dollars, cumulative tons and best HOD from different starting blocks and elevations.
• Enable an initial footprint to be established for flat or inclined extraction levels.
• Assess multilevel scenarios using maximum height of draw and replacing the material by default values for the upper level.
• Evaluate simple production schedules using vertical mining

The creation of a production schedule requires a defined sequence based on the shape of the cave front. This is created simply using an X-Y curve and applied with a certain direction (azimuth). An example of a production schedule using a sequence moving east in a V-shape is shown in Figure 3.

The option to create a mine sequence defining a shape and direction provides the opportunity to run many schedules to evaluate different scenarios. The option to start in a specific point and move in a circle to emulate a diamond shape is also available enabling all of the sequence options to be rapidly tested using Footprint Finder.

BEST AND WORST CASE CONCEPT

The concept of ‘best and worst case’ has been popular for open pit optimization for more than 15 years (Smith, 2001) using GEOVIA Whittle™. Whittle is able to generate a series of nested pits based on the economic values (grades, revenue factor and costs) defining limits on where to mine and when, however they do not identify a production schedule in terms of the optimal period in which a block should be mined. The best case scenario defines a schedule associated with mining a pushback completely before proceeding to the first bench in the subsequent pit. In this manner the highest value ore is mined as early as possible maximizing NPV. The worst case scenario defines a schedule where the entire bench across all pushbacks is mined prior to proceeding to the second bench. This results in pre-stripping the entire deposit, defers ore production and minimizes cash flow by placing stripping costs up front while delaying revenue opportunities.

The ‘best and worst case’ concept provides two nonoperational schedules, but defines a range of best and worst case scenarios to evaluate other operational options located in between and will provide the ability to assess them based on their delta from the best defined solution.

The same concept was adapted and implemented in a block caving mining environment to identify the best and worst sequence, based on the results obtained from Footprint Finder where each block column can be treated individually as a drawpoint to calculate its economic value based on the metal price, cost and grade and dilution profile, etc.

The sequence definition opens each block column using a certain shape and direction and thereby is suitable for block caving purposes where geotechnical, design and operational constraints need to be satisfied.

The best and worst case concept can be easily implemented in block cave mines to understand the maximum and minimum NPV, where the cash flow is calculated using a discount rate per year. The order of extraction of each column is very important and has a big impact over the NVP calculated. In this case, the best sequence will be the extraction of the column sorted from the highest to the lowest economic value and the worst sequence will be the opposite. Both cases are non-operational but provide a valid reference for planning purposes defining the maximum and minimum value of any operational sequence. Figure 4 describes an example of the application of this concept showing a plan view of the block model in Microsoft Excel™, where it is possible to see the best and worst sequence, based on the economic value of each block. Figure 5 demonstrates an example of the best and worst sequence concept and how other sequence options are located within this range. The opportunity to identify the value of the best option is an excellent reference for a mine planner when they are comparing different alternatives for a sequence.

If a sequence value is close to the best case, then there is little opportunity to improve the sequence. If the difference between best and worst cases is small, then the overall project itself is not sensitive to sequencing. A simple plot such as the one in Figure 5 is very useful when assessing the effectiveness of various sequences.

▶ In our next post​​​​​​​, we will provide an example of this concept in real footprint. Stay tuned!

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