MiningMath

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Get the NPV upper bound better than the Best Case scenario!

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Scenario tab

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General Parameters

MiningMath automatically switches to the Scenario Tab in the General option once a scenario is opened, as shown in Figure 1

The General tab presents all the general inputs regarding densities (Figure 1), economic parameters (Figure 2), slope angles (Figure 3) and stockpiles (Figure 4), which are detailed next.

Densities

Densities, as shown in Figure 1, are used along with block size to calculate tonnages. The user has two options to define them:

  • "Field" shows the column(s) that has/have been assigned to the density during the importation. This option is intended to allow varying densities by block.

  • "Default value" is applicable to any block without density information, whether a density column is imported or not. It is also used when you choose the field as .

Economic Parameters

The Discount Rate is a field of Economic parameters, as seen in Figure 2. It is usually considered in an annual base, is responsible to define the impact of mining ore/waste over time, which influences the algorithm decision-making process.

While working with different time frames, the discount rate serves just a rough NPV approximation, and it doesn’t affect so much the quality of the solution, given that the best materials would be allocated first. Thus, by multiplying or splitting it by the number of periods, you might get reasonable results.

Slope Angles

Slope angles are one of the most important parameters when considering constraints hierarchy. The user, as seen in Figure 3, has two options here:

  • Field shows the column(s) that has/have been assigned to the slope during the importation. This option is intended to allow different slope angles by block.

  • Default value is used to any block without slope information, even if a column was assigned. It is also used when you choose the field as <none> .

Stockpiling

The stockpiling feature can be used by activating the checkbox. When this option is enabled, shown in Figure 4, the user can define:

  • Fixed mining cost (cost/t) refers to the average mining cost used for the economic functionThis value is used to decompose the economic value while considering stockpiles.

  • Rehandling cost (cost/t) represents the cost to reclaim blocks from the stockpile to the process.

To illustrate the other tabs inside the Scenario tab, the parameters used in the Marvin case will be employed as summarized below:

Parameter Subparameter Value
Densities
Field
Density
Default value
2.75
Slope angles
Field
Slope
Default value
45 degrees
Stockpiling
Fixed mining cost
0.9$/t
Rehandling cost
0.2$/t
Discount rate

-

10%

Table 1: Parameters used in the Marvin cases.

Destinations: Process, Dump and Stockpile

Figure 5: Destinations tab, Recoveries for each element/mineral and destination, and Stockpile limit in tonnages.

On the Destinations tab (Figure 5), you will define destinations to where the blocks can be sent. Each target must be mapped with their respective field containing the economic values. MiningMath requires at least one destination for the process and one destination for the dump. For each destination, you have an economic value and recoveries by elements.

Process & Dump

To add destinations, in the bottom corner of the window, click on:

  • Add Process

  • Add Dump

Each scenario must contain at least one process and one dump among the destinations imported. The destination of each block will be reported by assigning them with the numbers 1 or 2 (see the numbers beside the Name column)which depends on the order of addition.

Recovery

For each processing stream, the user must inform a process recovery, varying from 0 to 1, to any element/mineral whose column has been imported as a grade.

This value on the interface serves only for the purpose of generating reports, as it has been considered during the economic calculation. Use the following values for the processing stream:

  • Cu: 0.88

  • Au: 0.60

Stockpile

You can also define a tonnage limit for the stockpile if activated in the General tab (see Figure 4).

MiningMath considers the tonnage inputted as a cumulative upper limit that will be considered all over the life of mine.

In this example, a limit has not been defined, which implies an capacity to stock. Read more about stockpiles.

Economic Value

In the column of Economic value, you must assign each destination to its corresponding economic function. Therefore, use:

  • Destination 1 - Process 1 - Economic Value Process

  • Destination 2 - Dump 1 - Economic Value Waste

Figure 6 zooms in the destination fields, showing how they should look like for this example.

Figure 6: Economic values for each destination.

Production Inputs

Figure 7: Production tab and production limits for each destination based on an yearly timeframe.

After completing the previous fields, move to the Production tab (Figure 7). You can define limits (in tonnes) for each destination and the total amount of material moved per period and also add different timeframe ranges in the optimization. For this example, use the values as shown in Figure 7.

  • TimeFrame: Years (1)

  • Process 1: 30,000,000 t

  • Dump 1: 50,000,000 t

  • Total: 80,000,000 t

Geometric Inputs

Figure 8: Operational constraints.

On the Geometric tab (Figure 8), you can define parameters intending to find mathematical solutions that already consider basic requirements to be operationally feasible. Figure 8 highlights Operational Fields, which could differ for each period range and timeframesuch as minimum widths and vertical rate. Optional Fields are also allowed. These allow the definition of: 1) areas to be forced and/or restricted; and 2) periods to which surfaces are applied. In this example the values defined for all periods are:

  • Minimum width: Mining 100m, Bottom: 100 m

  • Vertical rate of advance: Maximum 150 m

In the Geometric tab you can also force mining and restrict mining using surfaces based on coordinates and defined as a 3D-grid of points in the CSV format. Surfaces are the most important constraints within MiningMath’s hierarchy, allowing you to impose one’s understanding and take control of prior results and operational aspects.

Using surfaces, you are able to play with geotechnical aspects, force certain regions to allocate waste material, restrict areas to protect the environment, and/or guide operational aspects by importing a designed pit.

Due to the complexity of this subject, surfaces will be treated in a specific section of our documentation.

Average

Figure 9: Blending constraints.

On the Average tab, you are able to define a minimum and/or maximum average grades for any element/mineral imported as grade (Figure 9 area 1).

Blending constraints can also be defined by period ranges (Figure 9 area 2) and/or destination (Figure 9 area 3).

It’s worth mentioning that this minimum limit does not represent cut-off values. Since it is based on average parameters, the algorithm can use lower values to respect this parameter and increase the NPV with higher ones. If you wish to input a cut-off, a good way to do it is by filtering these blocks and assigning the the mass as a sum field, as mentioned here.

Sum

Figure 10: Other constraints.

On the Sum tab, you are able to consider any summed parameter as a minimum and/or maximum limits for any data imported as other (Figure 10 area 1).

Other constraints can also be defined by period ranges (Figure 10 area 2and/or destination (Figure 10 area 3).

This feature is available only at the full versions of MiningMath. Read more.

Overview

Click on Overview (Figure 11) for a single page summary of all parameters related to the direct block scheduling, as illustrated in the figure below.

The Save as option (Figure 12) can be used to redefine the name, description for an edited scenario, and its decision tree.

You can also decide which files MiningMath will produce as outputs by using the execution options (Figure 13) before clicking on “Run” your scenario.

CONTENTS

Protected: Imperial system

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In-depth MiningMath

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Theory Validation

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Guaranteed Solutions

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MiningMath Uniqueness

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Time Limit

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Tutorials

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Theory

Workflow

Formatting the Block Model

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